A330946 - OEIS

%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