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%I #7 Oct 25 2022 09:03:42
%S 1,2,4,5,8,10,11,16,20,22,23,25,31,32,40,44,46,47,50,55,59,62,64,80,
%T 88,92,94,97,100,103,110,115,118,121,124,125,127,128,137,155,160,176,
%U 179,184,188,194,197,200,206,220,230,233,235,236,242,248,250,253,254
%N Numbers whose prime indices have only prime numbers as their own prime indices.
%C 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.
%C Numbers whose prime indices are prime numbers are listed by A076610.
%e The terms together with their prime indices begin:
%e 1: {}
%e 2: {1}
%e 4: {1,1}
%e 5: {3}
%e 8: {1,1,1}
%e 10: {1,3}
%e 11: {5}
%e 16: {1,1,1,1}
%e 20: {1,1,3}
%e 22: {1,5}
%e 23: {9}
%e 25: {3,3}
%e 31: {11}
%e 32: {1,1,1,1,1}
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[100],And@@PrimeQ/@Join@@primeMS/@primeMS[#]&]
%Y Contains all elements of A000079.
%Y Contains all primes indexed by elements of A076610.
%Y A000040 lists the prime numbers.
%Y A056239 adds up prime indices, row-sums of A112798.
%Y Cf. A003961, A045966, A064988, A066207, A215366, A357977, A357980, A357983.
%K nonn
%O 1,2
%A _Gus Wiseman_, Oct 23 2022
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