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A325121
Sum of binary digits of the prime indices of n.
2
0, 1, 1, 2, 2, 2, 1, 3, 2, 3, 2, 3, 2, 2, 3, 4, 3, 3, 1, 4, 2, 3, 2, 4, 4, 3, 3, 3, 2, 4, 3, 5, 3, 4, 3, 4, 2, 2, 3, 5, 3, 3, 3, 4, 4, 3, 4, 5, 2, 5, 4, 4, 1, 4, 4, 4, 2, 3, 2, 5, 2, 4, 3, 6, 4, 4, 3, 5, 3, 4, 2, 5, 3, 3, 5, 3, 3, 4, 3, 6, 4, 4, 4, 4, 5, 4, 3
OFFSET
1,4
COMMENTS
The sum of binary digits of an integer is the number of 1's in its binary representation. 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
Totally additive with a(prime(n)) = A000120(n).
MATHEMATICA
Table[Sum[pr[[2]]*DigitCount[PrimePi[pr[[1]]], 2, 1], {pr, FactorInteger[n]}], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 29 2019
STATUS
approved