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A325122
Sum of binary digits of the prime indices of n, minus Omega(n).
2
0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 2, 0, 0, 1, 0, 1, 1, 0, 2, 1, 0, 0, 1, 1, 2, 0, 1, 2, 1, 0, 1, 0, 1, 1, 2, 0, 2, 1, 1, 1, 3, 0, 0, 2, 2, 1, 0, 0, 2, 0, 0, 1, 1, 1, 1, 2, 0, 0, 2, 1, 2, 2, 1, 1, 1, 0, 2, 1, 2, 0, 1, 1, 2, 1, 0, 2, 3, 0, 3, 2, 1
OFFSET
1,17
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)) = A048881(n).
MATHEMATICA
Table[Sum[pr[[2]]*(DigitCount[PrimePi[pr[[1]]], 2, 1]-1), {pr, If[n==1, {}, FactorInteger[n]]}], {n, 100}]
CROSSREFS
Positions of zeros are A318400.
Other totally additive sequences: A056239, A302242, A318994, A318995, A325033, A325034, A325120, A325121.
Sequence in context: A089224 A344987 A359325 * A234578 A069859 A179317
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 29 2019
STATUS
approved