cp's OEIS Frontend

A366848 Odd numbers whose odd prime indices are relatively prime.

%I A366848 #5 Nov 01 2023 10:00:49
%S A366848 55,85,155,165,187,205,253,255,275,295,335,341,385,391,415,425,451,
%T A366848 465,485,495,527,545,561,595,605,615,635,649,697,713,715,737,745,759,
%U A366848 765,775,785,799,803,825,885,895,913,935,943,955,1003,1005,1023,1025,1045
%N A366848 Odd numbers whose odd prime indices are relatively prime.
%C A366848 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 A366848 The odd prime indices of 345 are {3,9}, which are not relatively prime, so 345 is not in the sequence.
%e A366848 The odd prime indices of 825 are {3,3,5}, which are relatively prime, so 825 is in the sequence
%e A366848 The terms together with their prime indices begin:
%e A366848     55: {3,5}
%e A366848     85: {3,7}
%e A366848    155: {3,11}
%e A366848    165: {2,3,5}
%e A366848    187: {5,7}
%e A366848    205: {3,13}
%e A366848    253: {5,9}
%e A366848    255: {2,3,7}
%e A366848    275: {3,3,5}
%e A366848    295: {3,17}
%e A366848    335: {3,19}
%e A366848    341: {5,11}
%e A366848    385: {3,4,5}
%e A366848    391: {7,9}
%e A366848    415: {3,23}
%e A366848    425: {3,3,7}
%e A366848    451: {5,13}
%e A366848    465: {2,3,11}
%e A366848    485: {3,25}
%e A366848    495: {2,2,3,5}
%t A366848 Select[Range[1000], OddQ[#]&&GCD@@Select[PrimePi/@First/@FactorInteger[#], OddQ]==1&]
%Y A366848 Including even terms and prime indices gives A289509, ones of A289508, counted by A000837.
%Y A366848 Including even prime indices gives A302697, counted by A302698.
%Y A366848 Including even terms gives A366846, counted by A366850.
%Y A366848 For halved even instead of odd prime indices we have A366849.
%Y A366848 A000041 counts integer partitions, strict A000009 (also into odds).
%Y A366848 A066208 lists numbers with all odd prime indices, even A066207.
%Y A366848 A112798 lists prime indices, length A001222, sum A056239.
%Y A366848 A257991 counts odd prime indices, even A257992.
%Y A366848 A366528 adds up odd prime indices, partition triangle A113685.
%Y A366848 A366531 = 2*A366533 adds up even prime indices, triangle A113686/A174713.
%Y A366848 Cf. A000720, A018783, A055396, A061395, A087436, A325698, A365067, A366842, A366843, A366844, A366847.
%K A366848 nonn
%O A366848 1,1
%A A366848 _Gus Wiseman_, Nov 01 2023