A153730 a(n) = Sum_{m=1..n} A153452(m).

1, 2, 3, 4, 5, 7, 8, 9, 11, 14, 15, 18, 19, 23, 28, 29, 30, 35, 36, 42, 51, 56, 57, 61, 66, 72, 77, 87, 88, 104, 105, 106, 120, 127, 141, 150, 151, 159, 179, 189, 190, 225, 226, 241, 262, 271, 272, 277, 291, 312, 339, 360, 361, 375, 403, 423, 458, 468, 469

Offset: 1

Author

Naohiro Nomoto, Dec 31 2008

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A153452.

Programs

Maple

with(numtheory):
b:= proc(n) option remember; `if`(n=1, 1,
      add(b(n/q*`if`(q=2, 1, prevprime(q))), q=factorset(n)))
    end:
a:= proc(n) a(n):= b(n)+ `if`(n=1, 0, a(n-1)) end:
seq(a(n), n=1..100);  # Alois P. Heinz, Aug 09 2012

Mathematica

b[n_] := b[n] = If[n == 1, 1, Sum[b[n/q If[q == 2, 1, NextPrime[q, -1]]], {q, FactorInteger[n][[All, 1]]}]];
a[n_] := a[n] = b[n] + If[n == 1, 0, a[n - 1]];
Array[a, 100] (* Jean-François Alcover, Nov 20 2020, after Alois P. Heinz *)

Extensions

More terms from Alois P. Heinz, Aug 09 2012