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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 (list; graph; refs; listen; history; text; internal format)
 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 Antti Karttunen, Table of n, a(n) for n = 1..10000 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. Cf. A000005, A002033, A056239, A112798, A299702, A325780, A325781. Sequence in context: A161225 A174980 A277488 * A119513 A308454 A085815 Adjacent sequences: A325791 A325792 A325793 * A325795 A325796 A325797 KEYWORD sign,look,hear AUTHOR Gus Wiseman, May 23 2019 STATUS approved

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Last modified May 30 05:52 EDT 2023. Contains 363044 sequences. (Running on oeis4.)