cp's OEIS Frontend

A330949 Odd nonprime numbers whose prime indices are not all prime numbers.

%I A330949 #9 Jan 15 2020 00:25:42
%S A330949 21,35,39,49,57,63,65,69,77,87,91,95,105,111,115,117,119,129,133,141,
%T A330949 143,145,147,159,161,169,171,175,183,185,189,195,203,207,209,213,215,
%U A330949 217,219,221,231,235,237,245,247,253,259,261,265,267,273,285,287,291
%N A330949 Odd nonprime numbers whose prime indices are not all prime numbers.
%C A330949 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 A330949 Also MM-numbers of multiset partitions with at least two parts, not all of which are singletons (see example).
%e A330949 The sequence of terms together with their prime indices of prime indices begins:
%e A330949    21: {{1},{1,1}}
%e A330949    35: {{2},{1,1}}
%e A330949    39: {{1},{1,2}}
%e A330949    49: {{1,1},{1,1}}
%e A330949    57: {{1},{1,1,1}}
%e A330949    63: {{1},{1},{1,1}}
%e A330949    65: {{2},{1,2}}
%e A330949    69: {{1},{2,2}}
%e A330949    77: {{1,1},{3}}
%e A330949    87: {{1},{1,3}}
%e A330949    91: {{1,1},{1,2}}
%e A330949    95: {{2},{1,1,1}}
%e A330949   105: {{1},{2},{1,1}}
%e A330949   111: {{1},{1,1,2}}
%e A330949   115: {{2},{2,2}}
%e A330949   117: {{1},{1},{1,2}}
%e A330949   119: {{1,1},{4}}
%e A330949   129: {{1},{1,4}}
%e A330949   133: {{1,1},{1,1,1}}
%e A330949   141: {{1},{2,3}}
%t A330949 Select[Range[1,100,2],!PrimeQ[#]&&!And@@PrimeQ/@PrimePi/@First/@If[#==1,{},FactorInteger[#]]&]
%Y A330949 Complement of A106092 in A330945.
%Y A330949 Including even numbers gives A330948.
%Y A330949 Including primes gives A330946.
%Y A330949 The number of prime prime indices is given by A257994.
%Y A330949 The number of nonprime prime indices is given by A330944.
%Y A330949 Primes of prime index are A006450.
%Y A330949 Primes of nonprime index are A007821.
%Y A330949 Products of primes of prime index are A076610.
%Y A330949 Products of primes of nonprime index are A320628.
%Y A330949 The set S of numbers whose prime indices do not all belong to S is A324694.
%Y A330949 Cf. A000040, A000720, A001222, A018252, A056239, A112798, A302242, A320629, A320633, A330943, A330947.
%K A330949 nonn
%O A330949 1,1
%A A330949 _Gus Wiseman_, Jan 14 2020