A327156 a(n) = Product_{d|n, d>1} A008578(1+A286561(n,sigma(d))), where A286561(n,x) gives the highest exponent of x dividing n.

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 8, 1, 1, 1, 2, 1, 4, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 5, 1, 8, 1, 1, 1, 16, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 32, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 2, 1, 1, 1

Offset: 1

Author

Antti Karttunen, Sep 18 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A000040, A008578, A286561, A173441.

Cf. also A293514, A322312, A323155, A327154, A327155.

Programs

PARI

A327156(n) = { my(m=1,v); fordiv(n,d,if((d>1) && ((v = valuation(n,sigma(d)))>0), m *= prime(v))); (m); };

Formula

a(n) = Product_{d|n, d>1} A008578(1+A286561(n,sigma(d))), where sigma = A000203.

Other identities. For all n >= 1:

1+A001222(a(n)) = A173441(n).