A351926 a(n) = Sum_{d|n, p|n, (p^d)|n, p prime} p.

0, 2, 3, 4, 5, 5, 7, 4, 3, 7, 11, 7, 13, 9, 8, 6, 17, 8, 19, 9, 10, 13, 23, 9, 5, 15, 6, 11, 29, 10, 31, 6, 14, 19, 12, 10, 37, 21, 16, 9, 41, 12, 43, 15, 8, 25, 47, 11, 7, 12, 20, 17, 53, 11, 16, 11, 22, 31, 59, 12, 61, 33, 10, 6, 18, 16, 67, 21, 26, 14, 71, 12, 73, 39, 8, 23, 18

Offset

1,2

Links

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

Example

a(12) = 7; we have 2^1, 2^2 and 3^1 dividing 12, so a(12) = 2 + 2 + 3 = 7.

Maple

f:= proc(n) local F, t, s;
  s:= 0;
  F:= ifactors(n)[2];
  for t in F do
    s:= s + nops(select(i -> n mod i = 0, [$1..t[2]]))*t[1]
  od;
  s
end proc:
map(f, [$1..100]); # Robert Israel, Sep 28 2024

Mathematica

Table[d = Divisors[n]; Total@ Map[#*LengthWhile[#^d, Divisible[n, #] &] &, Select[d, PrimeQ]], {n, 120}] (* Michael De Vlieger, Sep 29 2024 *)

Prog

(PARI) a(n) = my(f=factor(n), d=divisors(f)); sum(k=1, #f~, sum(m=1, #d, if ((n % f[k, 1]^d[m]) == 0, f[k, 1]))); \\ Michel Marcus, Feb 26 2022

Crossrefs

Cf. A000005, A027748.

Sequence in context: A086993 A238714 A289311 * A345303 A345310 A029908

Adjacent sequences: A351923 A351924 A351925 * A351927 A351928 A351929

Keyword

nonn

Author

Wesley Ivan Hurt, Feb 25 2022

Status

approved