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| A005153
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Practical numbers: positive integers m such that every k <= sigma(m) is a sum of distinct divisors of m. Also called panarithmic numbers.
(history;
published version)
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#278 by N. J. A. Sloane at Sat Mar 23 20:02:37 EDT 2024
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#277 by Michael De Vlieger at Sat Mar 23 19:13:42 EDT 2024
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#276 by Michael De Vlieger at Sat Mar 23 19:13:39 EDT 2024
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Sai Teja Somu and Duc Van Khanh Tran, <a href="https://arxiv.org/abs/2403.13533">On Sums of Practical Numbers and Polygonal Numbers</a>, arXiv:2403.13533 [math.NT], 2024.
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#275 by Joerg Arndt at Sat Dec 30 10:56:41 EST 2023
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#274 by Paolo P. Lava at Sat Dec 30 07:51:38 EST 2023
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with(numtheory): with(combinat): P:=proc(n) local a, b, k, j, ok; a:=choose([op(divisors(n))]); b:=[]; for k from 1 to nops(a) do b:=[op(b), add(a[k][j], j=1..nops(a[k]))]; od; for j from 0 to n-1 do ok:=0; for k in b do if k=j then ok:=1; break; fi; od;
if ok=0 then break; fi; od; if ok=1 then n; fi; end:
seq(P(i), i=1..252); # Paolo P. Lava, Jun 13 2017
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#273 by Alois P. Heinz at Thu Oct 26 15:15:34 EDT 2023
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#272 by Michel Marcus at Thu Oct 26 03:00:08 EDT 2023
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Discussion
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| Thu Oct 26
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| Michel Marcus: I wonder about mathscinet link, maybe only MR4643065 ?
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| 03:24
| Michel Marcus: forget this discussion
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#271 by Michel Marcus at Thu Oct 26 02:59:52 EDT 2023
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Sai Teja Somu, Ting Hon Stanford Li, and Andrzej Kukla, <a href="http://math.colgate.edu/~integers/x68/x68.pdf">On Some Results on Practical Numbers</a>, INTEGERS, Volume 23, A68, 2023 [<a href="https://mathscinet.ams.org/mathscinet/relay-station?mr=4643065">MR4643065</a>].
Sai Teja Somu, Ting Hon Stanford Li, and Andrzej Kukla, <a href="http://math.colgate.edu/~integers/x68/x68.pdf">On Some Results on Practical Numbers</a>, INTEGERS, Volume 23, A68, 2023[<a href="https://mathscinet.ams.org/mathscinet/relay-station?mr=4643065">MR4643065</a>].
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Discussion
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| Thu Oct 26
| 03:00
| Michel Marcus: So between Sa and Sr
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#270 by Andrzej Kukla at Thu Oct 26 02:54:31 EDT 2023
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#269 by Andrzej Kukla at Thu Oct 26 01:53:59 EDT 2023
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Sai Teja Somu, Ting Hon Stanford Li, and Andrzej Kukla, <a href="http://math.colgate.edu/~integers/x68/x68.pdf">On Some Results on Practical Numbers</a>, INTEGERS, Volume 23, A68, 2023[<a href="https://mathscinet.ams.org/mathscinet/relay-station?mr=4643065">MR4643065</a>].
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