cp's OEIS Frontend

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

%I A357981 #7 Oct 25 2022 09:03:42
%S A357981 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 A357981 88,92,94,97,100,103,110,115,118,121,124,125,127,128,137,155,160,176,
%U A357981 179,184,188,194,197,200,206,220,230,233,235,236,242,248,250,253,254
%N A357981 Numbers whose prime indices have only prime numbers as their own prime indices.
%C A357981 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 A357981 Numbers whose prime indices are prime numbers are listed by A076610.
%e A357981 The terms together with their prime indices begin:
%e A357981      1: {}
%e A357981      2: {1}
%e A357981      4: {1,1}
%e A357981      5: {3}
%e A357981      8: {1,1,1}
%e A357981     10: {1,3}
%e A357981     11: {5}
%e A357981     16: {1,1,1,1}
%e A357981     20: {1,1,3}
%e A357981     22: {1,5}
%e A357981     23: {9}
%e A357981     25: {3,3}
%e A357981     31: {11}
%e A357981     32: {1,1,1,1,1}
%t A357981 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A357981 Select[Range[100],And@@PrimeQ/@Join@@primeMS/@primeMS[#]&]
%Y A357981 Contains all elements of A000079.
%Y A357981 Contains all primes indexed by elements of A076610.
%Y A357981 A000040 lists the prime numbers.
%Y A357981 A056239 adds up prime indices, row-sums of A112798.
%Y A357981 Cf. A003961, A045966, A064988, A066207, A215366, A357977, A357980, A357983.
%K A357981 nonn
%O A357981 1,2
%A A357981 _Gus Wiseman_, Oct 23 2022