A316854 Number of integer partitions of n whose reciprocal sum is the reciprocal of an integer.

1, 1, 1, 2, 1, 1, 1, 2, 3, 2, 2, 2, 1, 1, 1, 4, 2, 4, 1, 5, 1, 5, 1, 3, 4, 2, 5, 6, 5, 5, 4, 5, 5, 4, 8, 10, 9, 7, 5, 9, 10, 6, 12, 10, 8, 7, 6, 9, 13, 15, 8, 19, 13, 19, 19, 19, 18, 22, 26, 28, 28, 29, 22, 33, 29, 28, 38, 34, 26, 40, 32, 43, 39, 51, 38, 62, 46

Offset

1,4

Comments

The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.

Links

Giovanni Resta, Table of n, a(n) for n = 1..200 (first 100 terms from Robert G. Wilson v)

Example

The a(36) = 10 partitions:
  (36),
  (30,6), (24,12), (18,18),
  (12,12,12),
  (12,12,6,6),
  (15,10,4,4,3), (12,12,6,3,3), (12,8,8,6,2),
  (6,6,6,6,6,6).

Mathematica

Table[Length[Select[IntegerPartitions[n], IntegerQ[1/Sum[1/m, {m, #}]]&]], {n, 30}]
ric[n_, p_, s_] := If[n == 0, If[IntegerQ[1/s], c++], Do[If[s + 1/i <= 1, ric[n - i, Append[p, i], s + 1/i]], {i, Min[p[[-1]], n], 1, -1}]]; a[n_] := (c = 0; Do[ric[n - j, {j}, 1/j], {j, n}]; c); Array[a, 80] (* after Giovanni Resta in A316898, Robert G. Wilson v, Jul 23 2018 *)

Prog

(PARI) a(n)={my(s=0); forpart(p=n, if(frac(1/sum(i=1, #p, 1/p[i]))==0, s++)); s} \\ Andrew Howroyd, Jul 15 2018

Crossrefs

Cf. A000041, A051908, A058360, A316855, A316856, A316857.

Sequence in context: A039958 A029344 A375731 * A367759 A125769 A367799

Adjacent sequences: A316851 A316852 A316853 * A316855 A316856 A316857

Keyword

nonn

Author

Gus Wiseman, Jul 14 2018

Extensions

a(51)-a(77) from Giovanni Resta, Jul 15 2018

Status

approved