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A343938
Twice the number of prime factors of n minus the sum of prime indices of n, both counted with multiplicity.
4
0, 1, 0, 2, -1, 1, -2, 3, 0, 0, -3, 2, -4, -1, -1, 4, -5, 1, -6, 1, -2, -2, -7, 3, -2, -3, 0, 0, -8, 0, -9, 5, -3, -4, -3, 2, -10, -5, -4, 2, -11, -1, -12, -1, -1, -6, -13, 4, -4, -1, -5, -2, -14, 1, -4, 1, -6, -7, -15, 1, -16, -8, -2, 6, -5, -2, -17, -3, -7
OFFSET
1,4
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
Totally additive with a(prime(k)) = 2 - k.
EXAMPLE
For n = 1050 we have 5 prime indices {1,2,3,3,4}, so a(1050) = 10 - 13 = -3.
MATHEMATICA
Table[2*PrimeOmega[n]-Total[Cases[FactorInteger[n], {p_, k_}:>k*PrimePi[p]]], {n, 100}]
CROSSREFS
First appearances are the elements of A174090 except for 3.
Positions of zeros are A340387.
Positions of nonpositive terms are A344291.
Positions of nonnegative terms are A344296.
A001222 counts prime indices.
A056239 adds up prime indices.
A112798 lists prime indices.
Sequence in context: A191620 A214751 A306512 * A239397 A307884 A329221
KEYWORD
sign
AUTHOR
Gus Wiseman, Aug 04 2021
STATUS
approved