# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a316896 Showing 1-1 of 1 %I A316896 #7 Jul 16 2018 21:47:42 %S A316896 1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,1,0,0,1,0,3,0,1,0,1,1,2,3,2,2,1,2,2, %T A316896 2,3,5,5,2,2,5,5,9,3,4,6,4,3,6,8,4,10,9,8,11,7,13,12,15,15,21,18,16, %U A316896 21,19,17,30,23,19,23,28,25,29,34,29,44,28,46,48,42 %N A316896 Number of aperiodic integer partitions of n whose reciprocal sum is 1. %C A316896 The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k. %C A316896 A partition is aperiodic if its multiplicities are relatively prime. %H A316896 Gus Wiseman, Sequences counting and ranking integer partitions by their reciprocal sums %e A316896 The a(37) = 5 partitions are (24,8,3,2), (20,5,4,4,4), (15,10,6,3,3), (14,7,7,7,2), (10,10,10,5,2). %t A316896 Table[Length[Select[IntegerPartitions[n],And[GCD@@Length/@Split[#]==1,Sum[1/m,{m,#}]==1]&]],{n,30}] %Y A316896 Cf. A000837, A002966, A051908, A058360, A100953, A316854, A316888-A316904. %K A316896 nonn %O A316896 1,22 %A A316896 _Gus Wiseman_, Jul 16 2018 %E A316896 a(51)-a(80) from _Giovanni Resta_, Jul 16 2018 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE