A316891 - OEIS

A316891

Number of aperiodic integer partitions of n into relatively prime parts whose reciprocal sum is an integer.

%I #8 Jul 18 2018 19:20:37

%S 1,0,0,0,1,0,1,0,2,1,5,2,7,4,7,6,13,7,18,12,20,17,32,20,39,31,47,45,

%T 74,56,96,83,109,105,151,130,199,183,234,232,319,286,404,386,473,488,

%U 638,599,782,767,931,960,1197,1165,1465,1477,1747,1814,2212,2196

%N Number of aperiodic integer partitions of n into relatively prime parts whose reciprocal sum is an integer.

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

%C A partition is aperiodic if its multiplicities are relatively prime.

%H Gus Wiseman, <a href="/A051908/a051908.txt">Sequences counting and ranking integer partitions by their reciprocal sums</a>

%e The a(17) = 13 partitions:

%e (6443),

%e (44441),

%e (3332222), (6322211),

%e (44222111),

%e (222222221), (333221111), (632111111),

%e (4421111111),

%e (22222211111), (33311111111),

%e (2222111111111),

%e (221111111111111).

%t Table[Length[Select[IntegerPartitions[n],And[GCD@@#==1,GCD@@Length/@Split[#]==1,IntegerQ[Sum[1/m,{m,#}]]]&]],{n,50}]

%Y Cf. A000837, A002966, A051908, A058360, A100953, A316854, A316856, A316888-A316904.

%K nonn

%O 1,9

%A _Gus Wiseman_, Jul 16 2018

%E a(51)-a(60) from _Alois P. Heinz_, Jul 18 2018