A357981 Numbers whose prime indices have only prime numbers as their own prime indices.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 23, 25, 31, 32, 40, 44, 46, 47, 50, 55, 59, 62, 64, 80, 88, 92, 94, 97, 100, 103, 110, 115, 118, 121, 124, 125, 127, 128, 137, 155, 160, 176, 179, 184, 188, 194, 197, 200, 206, 220, 230, 233, 235, 236, 242, 248, 250, 253, 254

Offset: 1

Author

Gus Wiseman, Oct 23 2022

Keywords

• nonn

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.

Numbers whose prime indices are prime numbers are listed by A076610.

Examples

			The terms together with their prime indices begin:
     1: {}
     2: {1}
     4: {1,1}
     5: {3}
     8: {1,1,1}
    10: {1,3}
    11: {5}
    16: {1,1,1,1}
    20: {1,1,3}
    22: {1,5}
    23: {9}
    25: {3,3}
    31: {11}
    32: {1,1,1,1,1}
		

Crossrefs

Contains all elements of A000079.

Contains all primes indexed by elements of A076610.

A000040 lists the prime numbers.

A056239 adds up prime indices, row-sums of A112798.

Cf. A003961, A045966, A064988, A066207, A215366, A357977, A357980, A357983.

Programs

Mathematica

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],And@@PrimeQ/@Join@@primeMS/@primeMS[#]&]