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

1,2

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.

Links

Table of n, a(n) for n=1..59.

Example

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}

Mathematica

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

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.

Sequence in context: A244991 A004612 A066208 * A169743 A191986 A018699

Adjacent sequences: A357978 A357979 A357980 * A357982 A357983 A357984

Keyword

nonn

Author

Gus Wiseman, Oct 23 2022

Status

approved