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

Offset: 1

Author

Michael De Vlieger, Mar 24 2024

Keywords

• nonn
• easy

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

Intersection of A007310 and A126706.

Intersection of A007310, A013929, and A024619.