The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A309526

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a(n) is the greatest divisor of A001353(n) that is coprime to A001353(m) for all positive integers m < n.
(history; published version)

#9 by Peter Luschny at Wed Aug 14 14:11:48 EDT 2019

STATUS

reviewed

approved

#8 by Joerg Arndt at Wed Aug 14 11:16:31 EDT 2019

STATUS

proposed

reviewed

#7 by Jianing Song at Sat Aug 10 08:43:47 EDT 2019

STATUS

editing

proposed

#6 by Jianing Song at Sat Aug 10 08:37:11 EDT 2019

COMMENTS

Analog of A178763 and A308949.

CROSSREFS

Cf. A001353, A306825, A309040.

Cf. A178763, A308949, A309525.

#5 by Jianing Song at Sat Aug 10 08:26:23 EDT 2019

DATA

1, 4, 15, 7, 209, 13, 2911, 97, 901, 181, 564719, 193, 7865521, 2521, 6989, 18817, 1525870529, 2701, 21252634831, 37441, 6779137, 489061, 4122901604639, 37633, 274758906449, 6811741, 6575588101, 1037623, 11140078609864049, 40321, 155161278879431551

COMMENTS

Let b(n) = A309040(n)*gcd(A309040(n),n), then for n > 3: a(n) = b(2n) for even n and b(n)*b(2n) for odd n. It seems highly impossible that b(n) = 1 holds for n > 3, so it seems that only even-indexed terms can be primes.

FORMULA

a(n) = A306825(n) / gcd(A306825(n), n) if n != 2, 3.

EXAMPLE

A001353(6) = 780 = 2^2 * 3 * 5 * 13. We have 2 divides A001353(2) = 2 and 3, 5 divides A001353(3) = 15, but A001353(m) is coprime to 13 for all 1 <= m < 6, so a(6) = 13.

PROG

ab(n) = my(v=divisors(n)); prod(i=1, #v, T(v[i])^moebius(n/v[i]))

ba(n) = if(isprime(n)&&!(12%n), ab(n), ab(n)/gcd(n, ab(n)))

#4 by Jianing Song at Tue Aug 06 08:15:35 EDT 2019

PROG

(PARI) T(n) = ([4, -1; 1, 0]^n)[2, 1]

a(n) = my(v=divisors(n)); prod(i=1, #v, T(v[i])^moebius(n/v[i]))

b(n) = if(isprime(n)&&!(12%n), a(n), a(n)/gcd(n, a(n)))

#3 by Jianing Song at Tue Aug 06 08:10:19 EDT 2019

NAME

allocated a(n) is the greatest divisor of A001353(n) that is coprime to A001353(m) for Jianing Songall positive integers m < n.

DATA

1, 4, 15, 7, 209, 13

OFFSET

1,2

KEYWORD

allocated

nonn

AUTHOR

Jianing Song, Aug 06 2019

STATUS

approved

editing

#2 by Jianing Song at Tue Aug 06 08:09:09 EDT 2019

NAME

allocated for Jianing Song

KEYWORD

recycled

allocated

#1 by Russ Cox at Sun Jan 27 08:30:53 EST 2019

KEYWORD

recycled

STATUS

approved