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

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Eric Weisstein's World of Mathematics, Refactorable Number

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A284600 A114536 A330692 * A345992 A350333 A138010

Adjacent sequences: A349655 A349656 A349657 * A349659 A349660 A349661

Keyword

nonn

Author

Wesley Ivan Hurt, Nov 23 2021

Status

approved