A343197 Numbers k such that A025281(k) is prime.

2, 3, 6, 16, 29, 30, 34, 35, 36, 39, 57, 59, 76, 77, 88, 94, 101, 112, 126, 166, 177, 192, 206, 228, 238, 248, 251, 258, 259, 260, 271, 275, 276, 282, 299, 317, 318, 333, 345, 347, 353, 354, 370, 378, 386, 391, 402, 407, 417, 437, 445, 452, 455, 466, 470, 475, 478, 489, 494, 499, 508, 521, 530

Offset: 1

Author

J. M. Bergot and Robert Israel, Apr 07 2021

Keywords

• nonn

Comments

Numbers k such that A343196(k) = 1.

Examples

			a(4) = 16 is a term because A025281(16) = A001414(16!) = 101.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001414, A025281, A343196.

Programs

Maple

sopf:= proc(n) local t; add(t[1]*t[2],t=ifactors(n)[2]) end proc:
R:= NULL: count:= 0: T:= 0:
for n from 2 while count < 100 do
T:= T + sopf(n);
if isprime(T) then R:= R, n; count:= count+1 fi;
od:
R;

Mathematica

Select[Range[2, 530], PrimeQ@ Total@ Flatten[ConstantArray[#1, #2] & @@@ FactorInteger[#]] &[#!] &] (* Michael De Vlieger, Apr 07 2021 *)

Python

from sympy import isprime, factorint
A343197_list = [n for n in range(2,10**6) if isprime(sum(sum(p*e for p, e in factorint(i).items()) for i in range(2,n+1)))] # Chai Wah Wu, Apr 09 2021