cp's OEIS Frontend

A370804 Number of non-condensed integer partitions of n into parts > 1.

%I A370804 #12 Feb 14 2025 09:45:47
%S A370804 0,0,0,0,0,0,1,0,1,2,3,3,6,6,12,14,21,25,37,43,62,75,101,124,167,198,
%T A370804 261,316,401,488,618,745,930,1119,1379,1664,2032,2433,2960,3537,4259,
%U A370804 5076,6094,7227,8629,10205,12126,14302,16932,19893,23471,27502,32315,37775
%N A370804 Number of non-condensed integer partitions of n into parts > 1.
%C A370804 These are partitions without ones such that it is not possible to choose a different divisor of each part.
%e A370804 The a(6) = 1 through a(14) = 12 partitions:
%e A370804   (222)  .  (2222)  (333)   (3322)   (3332)   (3333)    (4333)    (4442)
%e A370804                     (3222)  (4222)   (5222)   (4422)    (7222)    (5333)
%e A370804                             (22222)  (32222)  (6222)    (33322)   (5522)
%e A370804                                               (33222)   (43222)   (8222)
%e A370804                                               (42222)   (52222)   (33332)
%e A370804                                               (222222)  (322222)  (43322)
%e A370804                                                                   (44222)
%e A370804                                                                   (53222)
%e A370804                                                                   (62222)
%e A370804                                                                   (332222)
%e A370804                                                                   (422222)
%e A370804                                                                   (2222222)
%t A370804 Table[Length[Select[IntegerPartitions[n],FreeQ[#,1] && Length[Select[Tuples[Divisors/@#],UnsameQ@@#&]]==0&]],{n,0,30}]
%Y A370804 These partitions have as ranks the odd terms of A355740.
%Y A370804 The version with ones is A370320, complement A239312.
%Y A370804 The complement without ones is A370805.
%Y A370804 The version for prime factors is A370807, with ones A370593.
%Y A370804 The version for factorizations is A370813, complement A370814.
%Y A370804 A000005 counts divisors.
%Y A370804 A000041 counts integer partitions, strict A000009.
%Y A370804 A027746 lists prime factors, A112798 indices, length A001222.
%Y A370804 A355731 counts choices of a divisor of each prime index, firsts A355732.
%Y A370804 A355741, A355744, A355745 choose prime factors of prime indices.
%Y A370804 Cf. A355529, A355739, A367867, A367901, A368110, A368413, A370595, A370806, A370808, A370810.
%K A370804 nonn
%O A370804 0,10
%A A370804 _Gus Wiseman_, Mar 03 2024
%E A370804 More terms from _Jinyuan Wang_, Feb 14 2025