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A357981
Numbers whose prime indices have only prime numbers as their own prime indices.
0
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.
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.
Sequence in context: A244991 A004612 A066208 * A169743 A191986 A018699
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 23 2022
STATUS
approved