cp's OEIS Frontend

A368728 Numbers whose prime indices are 1, prime, or semiprime.

%I A368728 #6 Jan 08 2024 14:30:37
%S A368728 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21,22,23,24,25,26,27,
%T A368728 28,29,30,31,32,33,34,35,36,39,40,41,42,43,44,45,46,47,48,49,50,51,52,
%U A368728 54,55,56,58,59,60,62,63,64,65,66,67,68,69,70,72,73,75
%N A368728 Numbers whose prime indices are 1, prime, or semiprime.
%C A368728 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.
%F A368728 Closed under multiplication.
%t A368728 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n], {p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A368728 Select[Range[100],Max@@Length/@prix/@prix[#]<=2&]
%Y A368728 These are products of primes indexed by elements of A037143.
%Y A368728 For just primes we have A076610, strict A302590.
%Y A368728 For just semiprimes we have A339112, strict A340020.
%Y A368728 For squarefree semiprimes we have A339113, strict A309356.
%Y A368728 The odd case is A368729, strict A340019.
%Y A368728 The complement is A368833.
%Y A368728 A000607 counts partitions into primes, A034891 with ones allowed.
%Y A368728 A001358 lists semiprimes, squarefree A006881.
%Y A368728 A006450, A106349, A322551, A368732 list selected primes.
%Y A368728 A056239 adds up prime indices, row sums of A112798.
%Y A368728 A101048 counts partitions into semiprimes.
%Y A368728 Cf. A000040, A000720, A001222, A003963, A005117, A302242, A320628, A320911, A320912.
%K A368728 nonn
%O A368728 1,2
%A A368728 _Gus Wiseman_, Jan 07 2024