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

7, 13, 19, 21, 23, 29, 35, 37, 39, 43, 47, 49, 53, 57, 61, 63, 65, 69, 71, 73, 77, 79, 87, 89, 91, 95, 97, 101, 103, 105, 107, 111, 113, 115, 117, 119, 129, 131, 133, 137, 139, 141, 143, 145, 147, 149, 151, 159, 161, 163, 167, 169, 171, 173, 175, 181, 183, 185

Offset

1,1

Comments

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.

Also MM-numbers of multiset partitions whose parts not all singletons (see example).

Links

Table of n, a(n) for n=1..58.

Example

The sequence of terms together with their prime indices of prime indices begins:
   7: {{1,1}}
  13: {{1,2}}
  19: {{1,1,1}}
  21: {{1},{1,1}}
  23: {{2,2}}
  29: {{1,3}}
  35: {{2},{1,1}}
  37: {{1,1,2}}
  39: {{1},{1,2}}
  43: {{1,4}}
  47: {{2,3}}
  49: {{1,1},{1,1}}
  53: {{1,1,1,1}}
  57: {{1},{1,1,1}}
  61: {{1,2,2}}
  63: {{1},{1},{1,1}}
  65: {{2},{1,2}}
  69: {{1},{2,2}}
  71: {{1,1,3}}
  73: {{2,4}}

Mathematica

Select[Range[1, 100, 2], !And@@PrimeQ/@PrimePi/@First/@If[#==1, {}, FactorInteger[#]]&]

Crossrefs

Odd numbers n such that A330944(n) > 0.

Including even numbers gives A330945.

The restriction to nonprimes is A330949.

Taking nonprimes instead of odds gives A330947.

The number of prime prime indices is given by A257994.

Primes of prime index are A006450.

Primes of nonprime index are A007821.

Products of primes of prime index are A076610.

Products of primes of nonprime index are A320628.

The set S of numbers whose prime indices do not all belong to S is A324694.

Cf. A000040, A000720, A001222, A018252, A056239, A112798, A302242, A320629, A330943, A330947, A330948.

Sequence in context: A173928 A304995 A339657 * A160007 A024613 A024606

Adjacent sequences: A330943 A330944 A330945 * A330947 A330948 A330949

Keyword

nonn

Author

Gus Wiseman, Jan 13 2020

Status

approved