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%I #5 Nov 01 2023 09:58:01
%S 3,9,15,21,27,33,39,45,51,57,63,69,75,81,87,91,93,99,105,111,117,123,
%T 129,135,141,147,153,159,165,171,177,183,189,195,201,203,207,213,219,
%U 225,231,237,243,247,249,255,261,267,273,279,285,291,297,301,303,309
%N Odd numbers whose halved even 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 even prime indices of 91 are {4,6}, halved {2,3}, which are relatively prime, so 91 is in the sequence.
%e The prime indices of 665 are {3,4,8}, even {4,8}, halved {2,4}, which are not relatively prime, so 665 is not in the sequence.
%e The terms together with their prime indices begin:
%e 3: {2}
%e 9: {2,2}
%e 15: {2,3}
%e 21: {2,4}
%e 27: {2,2,2}
%e 33: {2,5}
%e 39: {2,6}
%e 45: {2,2,3}
%e 51: {2,7}
%e 57: {2,8}
%e 63: {2,2,4}
%e 69: {2,9}
%e 75: {2,3,3}
%e 81: {2,2,2,2}
%e 87: {2,10}
%e 91: {4,6}
%e 93: {2,11}
%e 99: {2,2,5}
%t Select[Range[100], OddQ[#]&&GCD@@Select[PrimePi/@First/@FactorInteger[#], EvenQ]==2&]
%Y For odd instead of halved even prime indices we have A366848.
%Y A version for odd indices A366846, counted by A366850.
%Y This is the odd restriction of A366847, counted by A366845.
%Y A000041 counts integer partitions, strict A000009 (also into odds).
%Y A035363 counts partitions into all even parts, ranks A066207.
%Y A112798 lists prime indices, length A001222, sum A056239.
%Y A162641 counts even prime exponents, odd A162642.
%Y A257992 counts even prime indices, odd A257991.
%Y A289509 lists numbers with relatively prime prime indices, ones of A289508, counted by A000837.
%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, A302697, A325698, A366842, A366843.
%K nonn
%O 1,1
%A _Gus Wiseman_, Nov 01 2023
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