cp's OEIS Frontend

A330946 Odd numbers whose prime indices are not all prime numbers.

%I A330946 #8 Jan 14 2020 22:17:07
%S A330946 7,13,19,21,23,29,35,37,39,43,47,49,53,57,61,63,65,69,71,73,77,79,87,
%T A330946 89,91,95,97,101,103,105,107,111,113,115,117,119,129,131,133,137,139,
%U A330946 141,143,145,147,149,151,159,161,163,167,169,171,173,175,181,183,185
%N A330946 Odd numbers whose prime indices are not all prime numbers.
%C A330946 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.
%C A330946 Also MM-numbers of multiset partitions whose parts not all singletons (see example).
%e A330946 The sequence of terms together with their prime indices of prime indices begins:
%e A330946    7: {{1,1}}
%e A330946   13: {{1,2}}
%e A330946   19: {{1,1,1}}
%e A330946   21: {{1},{1,1}}
%e A330946   23: {{2,2}}
%e A330946   29: {{1,3}}
%e A330946   35: {{2},{1,1}}
%e A330946   37: {{1,1,2}}
%e A330946   39: {{1},{1,2}}
%e A330946   43: {{1,4}}
%e A330946   47: {{2,3}}
%e A330946   49: {{1,1},{1,1}}
%e A330946   53: {{1,1,1,1}}
%e A330946   57: {{1},{1,1,1}}
%e A330946   61: {{1,2,2}}
%e A330946   63: {{1},{1},{1,1}}
%e A330946   65: {{2},{1,2}}
%e A330946   69: {{1},{2,2}}
%e A330946   71: {{1,1,3}}
%e A330946   73: {{2,4}}
%t A330946 Select[Range[1,100,2],!And@@PrimeQ/@PrimePi/@First/@If[#==1,{},FactorInteger[#]]&]
%Y A330946 Odd numbers n such that A330944(n) > 0.
%Y A330946 Including even numbers gives A330945.
%Y A330946 The restriction to nonprimes is A330949.
%Y A330946 Taking nonprimes instead of odds gives A330947.
%Y A330946 The number of prime prime indices is given by A257994.
%Y A330946 Primes of prime index are A006450.
%Y A330946 Primes of nonprime index are A007821.
%Y A330946 Products of primes of prime index are A076610.
%Y A330946 Products of primes of nonprime index are A320628.
%Y A330946 The set S of numbers whose prime indices do not all belong to S is A324694.
%Y A330946 Cf. A000040, A000720, A001222, A018252, A056239, A112798, A302242, A320629, A330943, A330947, A330948.
%K A330946 nonn
%O A330946 1,1
%A A330946 _Gus Wiseman_, Jan 13 2020