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

21, 35, 39, 49, 57, 63, 65, 69, 77, 87, 91, 95, 105, 111, 115, 117, 119, 129, 133, 141, 143, 145, 147, 159, 161, 169, 171, 175, 183, 185, 189, 195, 203, 207, 209, 213, 215, 217, 219, 221, 231, 235, 237, 245, 247, 253, 259, 261, 265, 267, 273, 285, 287, 291

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 with at least two parts, not all of which are singletons (see example).

Links

Table of n, a(n) for n=1..54.

Example

The sequence of terms together with their prime indices of prime indices begins:
   21: {{1},{1,1}}
   35: {{2},{1,1}}
   39: {{1},{1,2}}
   49: {{1,1},{1,1}}
   57: {{1},{1,1,1}}
   63: {{1},{1},{1,1}}
   65: {{2},{1,2}}
   69: {{1},{2,2}}
   77: {{1,1},{3}}
   87: {{1},{1,3}}
   91: {{1,1},{1,2}}
   95: {{2},{1,1,1}}
  105: {{1},{2},{1,1}}
  111: {{1},{1,1,2}}
  115: {{2},{2,2}}
  117: {{1},{1},{1,2}}
  119: {{1,1},{4}}
  129: {{1},{1,4}}
  133: {{1,1},{1,1,1}}
  141: {{1},{2,3}}

Mathematica

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

Crossrefs

Complement of A106092 in A330945.

Including even numbers gives A330948.

Including primes gives A330946.

The number of prime prime indices is given by A257994.

The number of nonprime prime indices is given by A330944.

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, A320633, A330943, A330947.

Sequence in context: A008946 A095738 A216467 * A248020 A290435 A138227

Adjacent sequences: A330946 A330947 A330948 * A330950 A330951 A330952

Keyword

nonn

Author

Gus Wiseman, Jan 14 2020

Status

approved