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