A367771 - OEIS

%I #9 Dec 14 2023 08:57:10

%S 1,1,1,2,0,1,2,1,1,3,0,2,0,0,2,1,1,2,3,1,1,2,0,2,0,1,4,1,0,1,3,0,1,1,

%T 2,3,2,0,2,2,0,1,1,1,4,2,1,3,2,0,2,3,0,3,1,1,3,0,0,2,0,1,0,1,1,5,0,0,

%U 2,2,2,2,2,0,2,4,0,1,1,0,4,2,1,2,2,0,4

%N Number of ways to choose a different prime index of each prime index of 2n + 1.

%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 prime indices of prime indices of 427 = 2*213 + 1 are {{1,1},{1,2,2}}, with four ways to choose (1,2), so a(213) = 4.

%e The prime indices of prime indices of 1469 = 2*734 + 1 are {{1,2},{1,2,3}}, with four choices (1,2), (1,3), (2,1), (2,3), so a(734) = 4.

%t prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n], {p_,k_}:>Table[PrimePi[p],{k}]]]];

%t Table[Length[Select[Tuples[prix/@prix[2n+1]], UnsameQ@@#&]],{n,0,100}]

%Y The "extended" version below includes alternating zeros at even positions.

%Y Extended positions of zeros are A355529, binary A367907.

%Y The extended version for binary indices is A367905.

%Y Extended positions of nonzeros are A368100, binary A367906.

%Y Extended positions of ones are A368101, binary A367908.

%Y The extended version without distinctness is A355741, for multisets A355744.

%Y A058891 counts set-systems, covering A003465, connected A323818.

%Y A112798 lists prime indices, reverse A296150, length A001222, sum A056239.

%Y A124010 gives prime signature, sorted A118914, length A001221, sum A001222.

%Y Cf. A007716, A355739, A355740, A355745, A367901, A367902, A367903.

%K nonn

%O 0,4

%A _Gus Wiseman_, Dec 12 2023