cp's OEIS Frontend

A367107 Numbers m not divisible by prime(bigomega(m)). Heinz numbers of integer partitions whose length is not a part (counted by A229816).

%I A367107 #7 Nov 22 2023 08:17:41
%S A367107 3,4,5,7,8,10,11,12,13,14,16,17,18,19,22,23,24,25,26,27,28,29,31,32,
%T A367107 34,35,36,37,38,40,41,42,43,44,46,47,48,49,52,53,54,55,58,59,60,61,62,
%U A367107 63,64,65,66,67,68,71,72,73,74,76,77,78,79,80,81,82,83,85
%N A367107 Numbers m not divisible by prime(bigomega(m)). Heinz numbers of integer partitions whose length is not a part (counted by A229816).
%C A367107 The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). This gives a bijective correspondence between positive integers and integer partitions.
%t A367107 Select[Range[2,100],!Divisible[#,Prime[PrimeOmega[#]]]&]
%Y A367107 Partitions of this type are counted by A229816.
%Y A367107 The complement is A325761, counted by A002865.
%Y A367107 If length is not a subset-sum: A367225, count A367213, complement A367224.
%Y A367107 A005117 ranks strict integer partitions, counted by A000009.
%Y A367107 A066208 ranks partitions into odd parts, also counted by A000009.
%Y A367107 A112798 lists prime indices, reverse A296150, length A001222, sum A056239.
%Y A367107 A237667 counts sum-free partitions, ranks A364531.
%Y A367107 A237668 counts sum-full partitions, sum-free A364532.
%Y A367107 Cf. A000720, A088902, A093641, A106529, A110295, A325762.
%K A367107 nonn
%O A367107 1,1
%A A367107 _Gus Wiseman_, Nov 21 2023