cp's OEIS Frontend

A368833 Numbers whose prime indices are not 1, prime, or semiprime.

%I A368833 #6 Jan 08 2024 14:30:24
%S A368833 19,37,38,53,57,61,71,74,76,89,95,103,106,107,111,113,114,122,131,133,
%T A368833 142,148,151,152,159,171,173,178,181,183,185,190,193,197,206,209,212,
%U A368833 213,214,222,223,226,228,229,239,244,247,251,259,262,263,265,266,267
%N A368833 Numbers whose prime indices are not 1, prime, or semiprime.
%C A368833 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 A368833 The terms together with their prime indices begin:
%e A368833    19: {8}
%e A368833    37: {12}
%e A368833    38: {1,8}
%e A368833    53: {16}
%e A368833    57: {2,8}
%e A368833    61: {18}
%e A368833    71: {20}
%e A368833    74: {1,12}
%e A368833    76: {1,1,8}
%e A368833    89: {24}
%e A368833    95: {3,8}
%e A368833   103: {27}
%e A368833   106: {1,16}
%e A368833   107: {28}
%e A368833   111: {2,12}
%e A368833   113: {30}
%e A368833   114: {1,2,8}
%e A368833   122: {1,18}
%e A368833   131: {32}
%e A368833   133: {4,8}
%e A368833   142: {1,20}
%e A368833   148: {1,1,12}
%t A368833 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n], {p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A368833 Select[Range[100], Max@@PrimeOmega/@prix[#]>2&]
%Y A368833 These are non-products of primes indexed by elements of A037143.
%Y A368833 The complement for just primes is A076610, strict A302590.
%Y A368833 The complement for just semiprimes is A339112, strict A340020.
%Y A368833 The complement for just squarefree semiprimes is A339113, strict A309356.
%Y A368833 The complement is A368728.
%Y A368833 The complement for just primes and semiprimes is A368729, strict A340019.
%Y A368833 A000607 counts partitions into primes, with ones allowed A034891.
%Y A368833 A001358 lists semiprimes, squarefree A006881.
%Y A368833 A006450, A106349, A322551, A368732 list selected primes.
%Y A368833 A056239 adds up prime indices, row sums of A112798.
%Y A368833 A101048 counts partitions into semiprimes.
%Y A368833 Cf. A000040, A000720, A001222, A003963, A005117, A302242, A320628.
%K A368833 nonn
%O A368833 1,1
%A A368833 _Gus Wiseman_, Jan 08 2024