cp's OEIS Frontend

A370805 Number of condensed integer partitions of n into parts > 1.

%I A370805 #13 Feb 14 2025 09:46:04
%S A370805 1,0,1,1,2,2,3,4,6,6,9,11,15,18,22,27,34,41,51,62,75,90,109,129,153,
%T A370805 185,217,258,307,359,421,493,577,675,788,909,1062,1227,1418,1633,1894,
%U A370805 2169,2497,2860,3285,3754,4298,4894,5587,6359,7230,8215,9331,10567,11965
%N A370805 Number of condensed integer partitions of n into parts > 1.
%C A370805 These are partitions without ones such that it is possible to choose a different divisor of each part.
%e A370805 The a(0) = 1 through a(9) = 6 partitions:
%e A370805   ()  .  (2)  (3)  (4)    (5)    (6)    (7)      (8)      (9)
%e A370805                    (2,2)  (3,2)  (3,3)  (4,3)    (4,4)    (5,4)
%e A370805                                  (4,2)  (5,2)    (5,3)    (6,3)
%e A370805                                         (3,2,2)  (6,2)    (7,2)
%e A370805                                                  (3,3,2)  (4,3,2)
%e A370805                                                  (4,2,2)  (5,2,2)
%t A370805 Table[Length[Select[IntegerPartitions[n],FreeQ[#,1] && Length[Select[Tuples[Divisors/@#],UnsameQ@@#&]]>0&]],{n,0,30}]
%Y A370805 The version with ones is A239312, complement A370320.
%Y A370805 These partitions have as ranks the odd terms of A368110, complement A355740.
%Y A370805 The version for prime factors is A370592, complement A370593, post A370807.
%Y A370805 The complement without ones is A370804, ranked by the odd terms of A355740.
%Y A370805 The version for factorizations is A370814, complement A370813.
%Y A370805 A000005 counts divisors.
%Y A370805 A000041 counts integer partitions, strict A000009.
%Y A370805 A355731 counts choices of a divisor of each prime index, firsts A355732.
%Y A370805 Cf. A355529, A355739, A367867, A367901, A368110, A368413, A370595, A370806, A370808, A370810.
%K A370805 nonn
%O A370805 0,5
%A A370805 _Gus Wiseman_, Mar 04 2024
%E A370805 More terms from _Jinyuan Wang_, Feb 14 2025