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 A008481 If n = Product (p_j^k_j) then a(n) = Sum partition(k_j). 4
 0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 5, 1, 3, 1, 3, 2, 2, 1, 4, 2, 2, 3, 3, 1, 3, 1, 7, 2, 2, 2, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 1, 6, 2, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 4, 1, 2, 3, 11, 2, 3, 1, 3, 2, 3, 1, 5, 1, 2, 3, 3, 2, 3, 1, 6, 5, 2, 1, 4, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS a(n) is a function of the prime signature of n (cf. A025487). - Matthew Vandermast, Jun 24 2012 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 (first 10000 terms from Vincenzo Librandi) FORMULA Additive with a(p^e) = A000041(e); a(n) = A007814(A318312(n)). - Antti Karttunen, Aug 30 2018 MAPLE a:= n-> add(combinat[numbpart](i[2]), i=ifactors(n)[2]): seq(a(n), n=1..100);  # Alois P. Heinz, Aug 30 2018 MATHEMATICA Prepend[ Array[ Plus @@ (PartitionsP /@ Last[ Transpose[ FactorInteger[ # ] ] ])&, 100, 2 ], 0 ] (* Second program: *) Array[Total[PartitionsP /@ FactorInteger[#][[All, -1]] - Boole[# == 1]] &, 87] (* Michael De Vlieger, Sep 02 2018 *) PROG (PARI) A008481(n) = vecsum(apply(e -> numbpart(e), factor(n)[, 2])); \\ Antti Karttunen, Aug 30 2018 CROSSREFS Cf. A000041, A318312. Differs from A318473 for the first time at n=32, where a(32)=7, while A318473(32)=8. Sequence in context: A098893 A302037 A069248 * A318473 A127669 A323436 Adjacent sequences:  A008478 A008479 A008480 * A008482 A008483 A008484 KEYWORD nonn AUTHOR EXTENSIONS Term a(1) corrected from 1 to 0 (for an empty sum) by Antti Karttunen, Aug 30 2018 STATUS approved

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Last modified March 21 01:18 EDT 2019. Contains 321356 sequences. (Running on oeis4.)