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

1,5

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

Formula

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

Mathematica

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

Prog

(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]); };

Crossrefs

Cf. A000265, A000720, A003963, A366790.

Cf. also A336466.

Sequence in context: A029382 A073780 A124389 * A027023 A052371 A062278

Adjacent sequences: A366786 A366787 A366788 * A366790 A366791 A366792

Keyword

nonn,mult

Author

Antti Karttunen, Oct 23 2023

Status

approved