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 A318573 Numerator of the reciprocal sum of the integer partition with Heinz number n. 4
 0, 1, 1, 2, 1, 3, 1, 3, 1, 4, 1, 5, 1, 5, 5, 4, 1, 2, 1, 7, 3, 6, 1, 7, 2, 7, 3, 9, 1, 11, 1, 5, 7, 8, 7, 3, 1, 9, 2, 10, 1, 7, 1, 11, 4, 10, 1, 9, 1, 5, 9, 13, 1, 5, 8, 13, 5, 11, 1, 17, 1, 12, 5, 6, 1, 17, 1, 15, 11, 19, 1, 4, 1, 13, 7, 17, 9, 5, 1, 13, 2, 14, 1, 11, 10, 15, 3, 16, 1, 7, 5, 19, 13, 16, 11, 11, 1, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k. The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k). LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537 FORMULA If n = Product prime(x_i)^y_i is the prime factorization of n, then a(n) is the numerator of Sum y_i/x_i. MATHEMATICA Table[Sum[pr[[2]]/PrimePi[pr[[1]]], {pr, If[n==1, {}, FactorInteger[n]]}], {n, 100}]//Numerator PROG (PARI) A318573(n) = { my(f=factor(n)); numerator(sum(i=1, #f~, f[i, 2]/primepi(f[i, 1]))); }; \\ Antti Karttunen, Nov 17 2019 CROSSREFS Positions of 1's are A316857. Cf. A051908, A056239, A058360, A112798, A289506, A289507, A296150, A316854, A316855, A316856, A318574, A325704. Sequence in context: A327530 A084360 A082460 * A029227 A029214 A134460 Adjacent sequences:  A318570 A318571 A318572 * A318574 A318575 A318576 KEYWORD nonn,frac AUTHOR Gus Wiseman, Aug 29 2018 EXTENSIONS More terms from Antti Karttunen, Nov 17 2019 STATUS approved

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Last modified June 1 02:09 EDT 2020. Contains 334758 sequences. (Running on oeis4.)