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 A072720 #10 Jan 02 2019 11:40:28
%S A072720 1,1,2,3,5,6,10,11,15,17,23,24,34,35,43,47,57,58,73,74,91,96,112,113,
%T A072720 139,141,163,168,197,198,235,236,272,279,317,321,378,379,427,436,501,
%U A072720 502,575,576,653,666,742,743,851,853,952,963,1080,1081,1211,1216,1361
%N A072720 Number of partitions of n into parts which are each powers of a single number (which may vary between partitions).
%C A072720 First differs from A322912 at a(12) = 34, A322912(12) = 33.
%F A072720 a(n) = a(n-1) + A072721(n). a(p) = a(p-1)+1 for p prime.
%e A072720 a(6)=10 since 6 can be written as 6 (powers of 6), 5+1 (5), 4+1+1 (4 or 2), 3+3 (3), 3+1+1+1 (3), 4+2 (2), 2+2+2 (2), 2+2+1+1 (2), 2+1+1+1+1 (2) and 1+1+1+1+1+1 (powers of anything).
%e A072720 From _Gus Wiseman_, Jan 01 2019: (Start)
%e A072720 The a(1) = 1 through a(8) = 15 integer partitions:
%e A072720 (1) (2) (3) (4) (5) (6) (7) (8)
%e A072720 (11) (21) (22) (41) (33) (61) (44)
%e A072720 (111) (31) (221) (42) (331) (71)
%e A072720 (211) (311) (51) (421) (422)
%e A072720 (1111) (2111) (222) (511) (611)
%e A072720 (11111) (411) (2221) (2222)
%e A072720 (2211) (4111) (3311)
%e A072720 (3111) (22111) (4211)
%e A072720 (21111) (31111) (5111)
%e A072720 (111111) (211111) (22211)
%e A072720 (1111111) (41111)
%e A072720 (221111)
%e A072720 (311111)
%e A072720 (2111111)
%e A072720 (11111111)
%e A072720 (End)
%t A072720 radbase[n_]:=n^(1/GCD@@FactorInteger[n][[All,2]]);
%t A072720 Table[Length[Select[IntegerPartitions[n],SameQ@@radbase/@DeleteCases[#,1]&]],{n,30}] (* _Gus Wiseman_, Jan 01 2019 *)
%Y A072720 Cf. A000123, A005704, A005705, A005706, A072721.
%Y A072720 Cf. A018819, A023893, A052410, A102430, A322900, A322901, A322902, A322903, A322912.
%K A072720 nonn
%O A072720 0,3
%A A072720 _Henry Bottomley_, Jul 05 2002