A318573 Numerator of the reciprocal sum of the integer partition with Heinz number n.

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

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

Gus Wiseman, Sequences counting and ranking integer partitions by their reciprocal sums

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to Heinz numbers

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 * A344774 A029227 A029214

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