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A325794
Number of divisors of n minus the sum of prime indices of n.
9
1, 1, 0, 1, -1, 1, -2, 1, -1, 0, -3, 2, -4, -1, -1, 1, -5, 1, -6, 1, -2, -2, -7, 3, -3, -3, -2, 0, -8, 2, -9, 1, -3, -4, -3, 3, -10, -5, -4, 2, -11, 1, -12, -1, -1, -6, -13, 4, -5, -1, -5, -2, -14, 1, -4, 1, -6, -7, -15, 5, -16, -8, -2, 1, -5, 0, -17, -3, -7
OFFSET
1,7
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, with sum A056239(n).
LINKS
FORMULA
a(n) = A000005(n) - A056239(n).
MATHEMATICA
Table[DivisorSigma[0, n]-Total[Cases[FactorInteger[n], {p_, k_}:>PrimePi[p]*k]], {n, 100}]
PROG
(PARI)
A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i, 2] * primepi(f[i, 1]))); }
A325794(n) = (numdiv(n)-A056239(n)); \\ Antti Karttunen, May 26 2019
CROSSREFS
Positions of positive terms are A325795.
Positions of nonnegative terms are A325796.
Positions of negative terms are A325797.
Positions of nonpositive terms are A325798.
Positions of 1's are A325792.
Positions of 0's are A325793.
Positions of -1's are A325694.
Sequence in context: A161225 A174980 A277488 * A119513 A308454 A085815
KEYWORD
sign,look,hear
AUTHOR
Gus Wiseman, May 23 2019
STATUS
approved