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 A316854 Number of integer partitions of n whose reciprocal sum is the reciprocal of an integer. 31
 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 (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. 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: A178526 A039958 A029344 * A125769 A272084 A003023 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

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Last modified August 13 05:41 EDT 2020. Contains 336442 sequences. (Running on oeis4.)