cp's OEIS Frontend

A366849 Odd numbers whose halved even prime indices are relatively prime.

%I A366849 #5 Nov 01 2023 09:58:01
%S A366849 3,9,15,21,27,33,39,45,51,57,63,69,75,81,87,91,93,99,105,111,117,123,
%T A366849 129,135,141,147,153,159,165,171,177,183,189,195,201,203,207,213,219,
%U A366849 225,231,237,243,247,249,255,261,267,273,279,285,291,297,301,303,309
%N A366849 Odd numbers whose halved even prime indices are relatively prime.
%C A366849 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 A366849 The even prime indices of 91 are {4,6}, halved {2,3}, which are relatively prime, so 91 is in the sequence.
%e A366849 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 A366849 The terms together with their prime indices begin:
%e A366849    3: {2}
%e A366849    9: {2,2}
%e A366849   15: {2,3}
%e A366849   21: {2,4}
%e A366849   27: {2,2,2}
%e A366849   33: {2,5}
%e A366849   39: {2,6}
%e A366849   45: {2,2,3}
%e A366849   51: {2,7}
%e A366849   57: {2,8}
%e A366849   63: {2,2,4}
%e A366849   69: {2,9}
%e A366849   75: {2,3,3}
%e A366849   81: {2,2,2,2}
%e A366849   87: {2,10}
%e A366849   91: {4,6}
%e A366849   93: {2,11}
%e A366849   99: {2,2,5}
%t A366849 Select[Range[100], OddQ[#]&&GCD@@Select[PrimePi/@First/@FactorInteger[#], EvenQ]==2&]
%Y A366849 For odd instead of halved even prime indices we have A366848.
%Y A366849 A version for odd indices A366846, counted by A366850.
%Y A366849 This is the odd restriction of A366847, counted by A366845.
%Y A366849 A000041 counts integer partitions, strict A000009 (also into odds).
%Y A366849 A035363 counts partitions into all even parts, ranks A066207.
%Y A366849 A112798 lists prime indices, length A001222, sum A056239.
%Y A366849 A162641 counts even prime exponents, odd A162642.
%Y A366849 A257992 counts even prime indices, odd A257991.
%Y A366849 A289509 lists numbers with relatively prime prime indices, ones of A289508, counted by A000837.
%Y A366849 A366528 adds up odd prime indices, partition triangle A113685.
%Y A366849 A366531 = 2*A366533 adds up even prime indices, triangle A113686/A174713.
%Y A366849 Cf. A000720, A055396, A061395, A066208, A302697, A325698, A366842, A366843.
%K A366849 nonn
%O A366849 1,1
%A A366849 _Gus Wiseman_, Nov 01 2023