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%I #6 Jan 14 2020 22:17:14
%S 1,9,15,25,27,33,45,51,55,75,81,85,93,99,121,123,125,135,153,155,165,
%T 177,187,201,205,225,243,249,255,275,279,289,295,297,327,335,341,363,
%U 369,375,381,405,415,425,451,459,465,471,495,527,531,537,545,561,573
%N Nonprime numbers whose prime indices are 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.
%e The sequence of terms together with their prime indices of prime indices begins:
%e 1: {}
%e 9: {{1},{1}}
%e 15: {{1},{2}}
%e 25: {{2},{2}}
%e 27: {{1},{1},{1}}
%e 33: {{1},{3}}
%e 45: {{1},{1},{2}}
%e 51: {{1},{4}}
%e 55: {{2},{3}}
%e 75: {{1},{2},{2}}
%e 81: {{1},{1},{1},{1}}
%e 85: {{2},{4}}
%e 93: {{1},{5}}
%e 99: {{1},{1},{3}}
%e 121: {{3},{3}}
%e 123: {{1},{6}}
%e 125: {{2},{2},{2}}
%e 135: {{1},{1},{1},{2}}
%e 153: {{1},{1},{4}}
%e 155: {{2},{5}}
%t Select[Range[100],!PrimeQ[#]&&And@@PrimeQ/@PrimePi/@First/@If[#==1,{},FactorInteger[#]]&]
%Y Complement in A076610 of A000040.
%Y Complement in A018252 of A330948.
%Y Nonprime numbers n such that A330944(n) = 0.
%Y Taking odds instead of nonprimes gives A330946.
%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 Numbers whose prime indices are not all prime are A330945.
%Y Cf. A000720, A001222, A056239, A112798, A302242, A320629, A320633, A330949.
%K nonn
%O 1,2
%A _Gus Wiseman_, Jan 13 2020
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