This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A326670 #4 Jul 18 2019 06:18:56
%S A326670 1,1,1,1,2,2,3,3,5,4,6,6,8,7,10,9,13,12,15,16,23,22,27,31,41,41,50,57,
%T A326670 74,75,90,99,133,127,158,167,226,203,278,262,371,325,457,387,622,484,
%U A326670 715,606,969,672,1178,866,1428,1050,1776,1142,2276,1459,2514,1792
%N A326670 Number of strict integer partitions y of n such that the average of the set {2^(s - 1): s in y} is an integer.
%e A326670 The a(1) = 1 through a(12) = 6 partitions (A = 10, B = 11, C = 12):
%e A326670 (1) (2) (3) (4) (5) (6) (7) (8) (9) (A) (B) (C)
%e A326670 (32) (42) (43) (53) (54) (64) (65) (75)
%e A326670 (52) (62) (63) (73) (74) (84)
%e A326670 (72) (82) (83) (93)
%e A326670 (531) (92) (A2)
%e A326670 (731) (642)
%t A326670 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&IntegerQ[Mean[2^(#-1)]]&]],{n,30}]
%Y A326670 The non-strict case is A326671.
%Y A326670 Strict factorizations with integer average are A326668.
%Y A326670 Strict partitions with integer average are A102627.
%Y A326670 Cf. A001055, A051293, A067538, A102627, A326028, A326622, A326647, A326666, A326667.
%K A326670 nonn
%O A326670 1,5
%A A326670 _Gus Wiseman_, Jul 17 2019