A357981 - OEIS

%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