A327154 a(n) = Product_{d|n, d>1} A008578(1+A286561(sigma(n),d)), where A286561(n,d) gives the highest exponent of d dividing n.

1, 1, 1, 1, 1, 12, 1, 1, 1, 2, 1, 6, 1, 5, 2, 1, 1, 2, 1, 2, 1, 3, 1, 48, 1, 2, 1, 80, 1, 45, 1, 1, 2, 2, 1, 1, 1, 3, 1, 8, 1, 44, 1, 6, 2, 5, 1, 6, 1, 1, 3, 2, 1, 20, 1, 20, 1, 2, 1, 80, 1, 11, 1, 1, 1, 63, 1, 2, 2, 7, 1, 2, 1, 2, 1, 6, 1, 20, 1, 2, 1, 2, 1, 264, 1, 3, 2, 6, 1, 48, 2, 10, 1, 7, 2, 108, 1, 1, 2, 1, 1, 125, 1, 2, 2

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

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

Formula

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

Other identities. For all n >= 1:

1+A001222(a(n)) = A073802(n).

Prog

(PARI) A327154(n) = { my(m=1, s=sigma(n), v); fordiv(n, d, if((d>1) && ((v = valuation(s, d))>0), m *= prime(v))); (m); };

Crossrefs

Cf. A000040, A008578, A286561, A073802.

Cf. also A293514, A322312, A323155, A327155, A327156.

Sequence in context: A325827 A010208 A306682 * A334731 A335948 A010209

Adjacent sequences: A327151 A327152 A327153 * A327155 A327156 A327157

Keyword

nonn

Author

Antti Karttunen, Sep 18 2019

Status

approved