A329037 a(n) = Product_{d|n, d>1} A008578(1+A286561(A276086(n),d)), where A286561(x,d) gives the exponent of the highest power of d dividing x.

1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 12, 1, 1, 1, 1, 5, 2, 1, 1, 1, 21, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 2, 1, 1, 12, 1, 1, 1, 2, 10, 2, 1, 1, 1, 7, 2, 2, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 2, 12, 1, 1, 1, 1, 48, 1, 3, 1, 1, 5, 2, 1, 1, 3, 7, 1, 2, 1, 1, 1, 5, 1, 2, 1, 1, 1, 1, 10, 2, 2, 1, 1, 1, 1, 720

Offset: 1

Author

Antti Karttunen, Nov 08 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to primorial base

Crossrefs

Cf. A008578, A276086, A286561, A327168.

Cf. also A327167.

Programs

PARI

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A329037(n) = { my(m=1,x=A276086(n),v); fordiv(n,d,if((d>1) && ((v = valuation(x,d))>0), m *= prime(v))); (m); };

Formula

a(n) = Product_{d|n, d>1} A008578(1+A286561(A276086(n),d)).

1+A001222(a(n)) = A327168(n).