cp's OEIS Frontend

A379317 Positive integers with a unique even prime index.

%I A379317 #5 Jan 01 2025 09:54:53
%S A379317 3,6,7,12,13,14,15,19,24,26,28,29,30,33,35,37,38,43,48,51,52,53,56,58,
%T A379317 60,61,65,66,69,70,71,74,75,76,77,79,86,89,93,95,96,101,102,104,106,
%U A379317 107,112,113,116,119,120,122,123,130,131,132,138,139,140,141,142
%N A379317 Positive integers with a unique even prime index.
%C A379317 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 A379317 The terms together with their prime indices begin:
%e A379317    3: {2}
%e A379317    6: {1,2}
%e A379317    7: {4}
%e A379317   12: {1,1,2}
%e A379317   13: {6}
%e A379317   14: {1,4}
%e A379317   15: {2,3}
%e A379317   19: {8}
%e A379317   24: {1,1,1,2}
%e A379317   26: {1,6}
%e A379317   28: {1,1,4}
%e A379317   29: {10}
%e A379317   30: {1,2,3}
%e A379317   33: {2,5}
%e A379317   35: {3,4}
%e A379317   37: {12}
%e A379317   38: {1,8}
%e A379317   43: {14}
%e A379317   48: {1,1,1,1,2}
%t A379317 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A379317 Select[Range[100],Length[Select[prix[#],EvenQ]]==1&]
%Y A379317 Partitions of this type are counted by A038348 (strict A096911).
%Y A379317 For all even parts we have A066207, counted by A035363 (strict A000700).
%Y A379317 For no even parts we have A066208, counted by A000009 (strict A035457).
%Y A379317 Positions of 1 in A257992.
%Y A379317 A000040 lists the primes, differences A001223.
%Y A379317 A055396 gives least prime index, greatest A061395.
%Y A379317 A056239 adds up prime indices, row sums of A112798, counted by A001222.
%Y A379317 Other counts of prime indices:
%Y A379317 - A257991 odd, see A000041, A000070, A349158.
%Y A379317 - A257994 prime, see A002095, A096258, A320628, A331386, A331915, A379304, A379305.
%Y A379317 - A330944 nonprime, see A000586, A000607, A076610, A330945.
%Y A379317 - A379300 composite, see A023895, A034891, A036497, A302540, A379301.
%Y A379317 - A379311 old prime, see A204389, A320629, A379312-A379315.
%Y A379317 Cf. A000720, A038550, A087436.
%K A379317 nonn
%O A379317 1,1
%A A379317 _Gus Wiseman_, Dec 29 2024