A318574 Denominator of the reciprocal sum of the integer partition with Heinz number n.

1, 1, 2, 1, 3, 2, 4, 1, 1, 3, 5, 2, 6, 4, 6, 1, 7, 1, 8, 3, 4, 5, 9, 2, 3, 6, 2, 4, 10, 6, 11, 1, 10, 7, 12, 1, 12, 8, 3, 3, 13, 4, 14, 5, 3, 9, 15, 2, 2, 3, 14, 6, 16, 2, 15, 4, 8, 10, 17, 6, 18, 11, 4, 1, 2, 10, 19, 7, 18, 12, 20, 1, 21, 12, 6, 8, 20, 3, 22

Offset

1,3

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

Table of n, a(n) for n=1..79.

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

Formula

If n = Product prime(x_i)^y_i is the prime factorization of n, then a(n) is the denominator of Sum y_i/x_i.

Mathematica

Table[Sum[pr[[2]]/PrimePi[pr[[1]]], {pr, If[n==1, {}, FactorInteger[n]]}], {n, 100}]//Denominator

Crossrefs

Positions of 1's are A316856.

Cf. A051908, A056239, A058360, A112798, A289506, A289507, A296150, A316854, A316855, A316857, A318573.

Sequence in context: A243561 A135550 A035491 * A277564 A363489 A363944

Adjacent sequences: A318571 A318572 A318573 * A318575 A318576 A318577

Keyword

nonn,frac

Author

Gus Wiseman, Aug 29 2018

Status

approved