A369954 - OEIS

A369954

Numbers k that are neither squarefree nor prime powers and also coprime to 6.

175, 245, 275, 325, 425, 475, 539, 575, 605, 637, 725, 775, 833, 845, 847, 875, 925, 931, 1025, 1075, 1127, 1175, 1183, 1225, 1325, 1375, 1421, 1445, 1475, 1519, 1525, 1573, 1625, 1675, 1715, 1775, 1805, 1813, 1825, 1859, 1925, 1975, 2009, 2023, 2057, 2075, 2107

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OFFSET

1,1

COMMENTS

Define quality Q to signify a number k neither squarefree nor prime power, i.e., k is in A126706. For example, 12 has quality Q but numbers k = 1..11 do not.

Numbers k in this sequence have quality Q and are such that either (k-1) or (k+1) also have quality Q. Hence k also appears in A369276, but not in A369516.

Numbers k such that k mod 12 = 1 or k mod 12 = 5 imply (k-1) in A126706, since 4 divides (k-1).

Numbers k such that k mod 12 = 7 or k mod 12 = 11 imply (k+1) in A126706, since 4 divides (k+1).

Proper subset of A367455.

By definition these odd numbers are such that A053669(k) = 2, therefore A053669(k) < A003557(k), hence this sequence is a proper subset of A360765.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

FORMULA

Intersection of A007310 and A126706.

Intersection of A007310, A013929, and A024619.

MATHEMATICA

Select[Flatten[Array[6 # + {1, 5} &, 360]], Nor[PrimePowerQ[#], SquareFreeQ[#]] &]

PROG

(PARI) isok(k) = !issquarefree(k) && !isprimepower(k) && (gcd(k, 6)==1); \\ Michel Marcus, Mar 25 2024

CROSSREFS

Cf. A003557, A007310, A008586, A013929, A024619, A053669, A126706, A356322, A369276, A360765, A367455, A369516.

Sequence in context: A045145 A351720 A015806 * A109836 A332047 A186211

Adjacent sequences: A369951 A369952 A369953 * A369955 A369956 A369957

KEYWORD

nonn,easy

AUTHOR

Michael De Vlieger, Mar 24 2024

STATUS

approved