A376514 Number of divisors of n that are neither squarefree nor prime powers.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 3, 0, 1, 0, 1, 0, 2, 0, 2, 0, 0, 0, 3, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 5, 0, 0, 1, 1, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0

Offset

1,24

Comments

This sequence is distinct from both A062977 and A335460.

A062977(36) = 0 while a(36) = 3 = card({12, 18, 36}).

A335460(60) = 6 while a(60) = 3 = card({12, 20, 60}).

Links

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

Formula

a(n) = tau(n) - 2^omega(n) - bigomega(n) + omega(n).

a(n) = A000005(n) - 2^A001221(n) - A001222(n) + A001221(n).

a(n) = A000005(n) - 2^A001221(n) - A046660(n).

Intersection of row n of A027750 and A126706.

a(n) > 0 for n in A126706.

Mathematica

{0}~Join~Table[DivisorSigma[0, n] - Total@ #1 - 2^#2 + #2 & @@ {#, Length[#]} &[FactorInteger[n][[All, -1]] ], {n, 2, 120}] (* or *)
Table[DivisorSum[n, 1 &, Nor[PrimePowerQ[#], SquareFreeQ[#]] &], {n, 120}]

Crossrefs

Cf. A000005, A001221, A001222, A027750, A046660, A126706, A376504.

Sequence in context: A076948 A255309 A335446 * A335460 A367077 A368073

Adjacent sequences: A376511 A376512 A376513 * A376515 A376516 A376517

Keyword

nonn,easy

Author

Michael De Vlieger, Sep 25 2024

Status

approved