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A325035
Product of sums of the multisets of prime indices of each prime index of 2 * n + 1.
4
1, 1, 2, 2, 1, 3, 3, 2, 4, 3, 2, 4, 4, 1, 4, 5, 3, 4, 4, 3, 6, 5, 2, 5, 4, 4, 4, 6, 3, 7, 5, 2, 6, 8, 4, 5, 6, 4, 6, 6, 1, 9, 8, 4, 5, 6, 5, 6, 6, 3, 7, 6, 4, 6, 10, 4, 6, 8, 3, 8, 9, 6, 8, 11, 5, 5, 6, 2, 7, 8, 5, 9, 8, 4, 7, 6, 4, 10, 12, 4, 8, 9, 6, 8, 9, 3
OFFSET
0,3
COMMENTS
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
FORMULA
Fully multiplicative with a(prime(n)) = A056239(n), restricted to odd n.
EXAMPLE
91 has prime indices {4,6} with prime indices {{1,1},{1,2}} with sums {2,3} with product a(45) = 6.
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Times@@Plus@@@primeMS/@primeMS[n], {n, 1, 200, 2}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 25 2019
STATUS
approved