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%I #9 Nov 01 2023 10:02:09
%S 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,
%T 50,52,54,55,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,85,86,88,90,
%U 92,94,96,98,100,102,104,106,108,110,112,114,116,118,120,122
%N Numbers whose odd prime indices are relatively prime.
%C A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%e The odd prime indices of 115 are {3,9}, and these are not relatively prime, so 115 is not in the sequence.
%e The odd prime indices of 825 are {3,3,5}, and these are relatively prime, so 825 is in the sequence.
%t Select[Range[100], GCD@@Select[PrimePi/@First/@FactorInteger[#], OddQ]==1&]
%Y Including even indices gives A289509, ones of A289508, counted by A000837.
%Y The complement when including even indices is A318978, counted by A018783.
%Y The nonzero complement ranks the partitions counted by A366842.
%Y The version for halved even indices is A366847.
%Y The odd case is A366848.
%Y The partitions with these Heinz numbers are counted by A366850.
%Y A000041 counts integer partitions, strict A000009 (also into odds).
%Y A112798 lists prime indices, length A001222, sum A056239.
%Y A257992 counts even prime indices, odd A257991.
%Y A366528 adds up odd prime indices, partition triangle A113685.
%Y A366531 = 2*A366533 adds up even prime indices, triangle A113686/A174713.
%Y Cf. A000720, A055396, A061395, A066208, A087436, A302696, A302697, A325698, A366843, A366844, A366849.
%K nonn
%O 1,1
%A _Gus Wiseman_, Oct 29 2023
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