A349658 Number of nonrefactorable divisors of n.

0, 0, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 3, 2, 1, 2, 1, 4, 3, 2, 1, 3, 2, 2, 2, 4, 1, 6, 1, 3, 3, 2, 3, 3, 1, 2, 3, 4, 1, 6, 1, 4, 4, 2, 1, 5, 2, 4, 3, 4, 1, 4, 3, 4, 3, 2, 1, 8, 1, 2, 4, 4, 3, 6, 1, 4, 3, 6, 1, 3, 1, 2, 5, 4, 3, 6, 1, 5, 3, 2, 1, 8, 3, 2, 3, 4, 1, 8, 3, 4

Offset: 1

Author

Wesley Ivan Hurt, Nov 23 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Eric Weisstein's World of Mathematics, Refactorable Number

Crossrefs

Cf. A000005, A033950, A336041, A335182, A349322.

Programs

Mathematica

a[n_] := DivisorSum[n, 1 &, !Divisible[#, DivisorSigma[0, #]] &]; Array[a, 100] (* Amiram Eldar, Nov 24 2021 *)

PARI

a(n) = sumdiv(n, d, d%numdiv(d) != 0); \\ Michel Marcus, Nov 24 2021

Formula

a(n) = A000005(n) - A336041(n).

a(n) = A349322(n) - A335182(n). - Antti Karttunen, Nov 24 2021

a(p) = 1 for odd primes p. - Wesley Ivan Hurt, Nov 28 2021