A366789 Fully multiplicative with a(p) = oddpart(primepi(p)).

1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 5, 1, 3, 1, 3, 1, 7, 1, 1, 3, 1, 5, 9, 1, 9, 3, 1, 1, 5, 3, 11, 1, 5, 7, 3, 1, 3, 1, 3, 3, 13, 1, 7, 5, 3, 9, 15, 1, 1, 9, 7, 3, 1, 1, 15, 1, 1, 5, 17, 3, 9, 11, 1, 1, 9, 5, 19, 7, 9, 3, 5, 1, 21, 3, 9, 1, 5, 3, 11, 3, 1, 13, 23, 1, 21, 7, 5, 5, 3, 3, 3, 9, 11, 15, 3, 1, 25, 1, 5, 9

Offset: 1

Author

Antti Karttunen, Oct 23 2023

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..52711
• Index entries for sequences related to prime indices in the factorization of n

Crossrefs

Cf. A000265, A000720, A003963, A366790.

Cf. also A336466.

Programs

Mathematica

{1}~Join~Array[#/2^IntegerExponent[#, 2] &@ Apply[Times, PrimePi[#1]^#2 & @@@ FactorInteger[#]] &, 120, 2] (* Michael De Vlieger, Oct 23 2023 *)

PARI

A000265(n) = (n>>valuation(n,2));
A366789(n) = { my(f=factor(n)); prod(k=1, #f~, A000265(primepi(f[k, 1]))^f[k, 2]); };

Formula

a(n) = A000265(A003963(n)).