cp's OEIS Frontend

A366847 Numbers whose halved even prime indices are nonempty and relatively prime.

%I A366847 #7 Nov 01 2023 10:01:09
%S A366847 3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,72,
%T A366847 75,78,81,84,87,90,91,93,96,99,102,105,108,111,114,117,120,123,126,
%U A366847 129,132,135,138,141,144,147,150,153,156,159,162,165,168,171,174
%N A366847 Numbers whose halved even prime indices are nonempty and relatively prime.
%C A366847 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.
%C A366847 Consists of powers of 2 times elements of the odd restriction A366849.
%e A366847 The even prime indices of 91 are {4,6}, halved {2,3}, which are relatively prime, so 91 is in the sequence.
%e A366847 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 A366847 The terms together with their prime indices begin:
%e A366847     3: {2}
%e A366847     6: {1,2}
%e A366847     9: {2,2}
%e A366847    12: {1,1,2}
%e A366847    15: {2,3}
%e A366847    18: {1,2,2}
%e A366847    21: {2,4}
%e A366847    24: {1,1,1,2}
%e A366847    27: {2,2,2}
%e A366847    30: {1,2,3}
%e A366847    33: {2,5}
%e A366847    36: {1,1,2,2}
%e A366847    39: {2,6}
%e A366847    42: {1,2,4}
%e A366847    45: {2,2,3}
%e A366847    48: {1,1,1,1,2}
%t A366847 Select[Range[100],GCD@@Select[PrimePi/@First/@FactorInteger[#],EvenQ]/2==1&]
%Y A366847 Including odd indices gives A289509, ones of A289508, counted by A000837.
%Y A366847 The complement including odd indices is A318978, counted by A018783.
%Y A366847 The partitions with these ranks are counted by A366845.
%Y A366847 A version for odd indices A366846, counted by A366850.
%Y A366847 The odd restriction is A366849.
%Y A366847 A000041 counts integer partitions, strict A000009 (also into odds).
%Y A366847 A035363 counts partitions into all even parts, ranks A066207.
%Y A366847 A112798 lists prime indices, length A001222, sum A056239.
%Y A366847 A162641 counts even prime exponents, odd A162642.
%Y A366847 A257992 counts even prime indices, odd A257991.
%Y A366847 A366528 adds up odd prime indices, partition triangle A113685.
%Y A366847 A366531 = 2*A366533 adds up even prime indices, triangle A113686/A174713.
%Y A366847 Cf. A000720, A055396, A061395, A066208, A168532, A302696, A302697, A325698, A366842, A366843, A366844, A366848.
%K A366847 nonn
%O A366847 1,1
%A A366847 _Gus Wiseman_, Oct 31 2023