A343416 a(n) = A001414(n) + A000203(n) + A001414(A000203(n)) + A000203(A001414(n)).

1, 11, 15, 25, 22, 30, 29, 41, 44, 41, 42, 54, 50, 55, 56, 85, 61, 78, 68, 76, 70, 73, 80, 94, 90, 93, 73, 92, 99, 112, 105, 104, 97, 104, 99, 139, 134, 125, 116, 126, 137, 149, 146, 137, 119, 140, 154, 182, 117, 167, 146, 149, 172, 157, 131, 161, 151, 166, 191, 224, 218, 190, 150, 294, 155, 205

Offset: 1

Author

J. M. Bergot and Robert Israel, Apr 14 2021

Keywords

• nonn

Comments

If n = prime(k) is prime, a(n) = 3*prime(k)+1+A210934(k).

Examples

			For n = 3, A001414(3) = 3, A000203(3) = A000203(A001414(3)) = 4 and A001414(A000203(3)) = 4, so a(3) = 3+4+4+4 = 15.
		

Links

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

Crossrefs

Cf. A000203, A001414, A210934.

Programs

Maple

spf:= proc(n) local t; add(t[1]*t[2],t=ifactors(n)[2]) end proc:
f:= proc(n) local a,b;
  a:= spf(n);
  b:= numtheory:-sigma(n);
  a+b+spf(b)+numtheory:-sigma(a)
end proc:
map(f, [$1..100]);