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A327155
a(n) = Product_{d|sigma(n), d>1} A008578(1+A286561(n,d)), where A286561(n,d) gives the highest exponent of d dividing n.
4
1, 1, 1, 1, 1, 8, 1, 1, 1, 2, 1, 6, 1, 2, 2, 1, 1, 3, 1, 3, 1, 2, 1, 80, 1, 2, 1, 48, 1, 8, 1, 1, 2, 2, 1, 1, 1, 2, 1, 20, 1, 8, 1, 6, 3, 2, 1, 21, 1, 1, 2, 3, 1, 20, 1, 20, 1, 2, 1, 48, 1, 2, 1, 1, 1, 8, 1, 3, 2, 2, 1, 3, 1, 2, 1, 6, 1, 8, 1, 7, 1, 2, 1, 48, 1, 2, 2, 10, 1, 48, 2, 6, 1, 2, 2, 264, 1, 1, 3, 1, 1, 8, 1, 5, 2
OFFSET
1,6
FORMULA
a(n) = Product_{d|sigma(n), d>1} A008578(1+A286561(n,d)), where sigma = A000203.
Other identities. For all n >= 1:
1+A001222(a(n)) = A073802(n).
PROG
(PARI) A327155(n) = { my(m=1, v); fordiv(sigma(n), d, if((d>1) && ((v = valuation(n, d))>0), m *= prime(v))); (m); };
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 18 2019
STATUS
approved