A153730 - OEIS

%I #14 Nov 20 2020 05:34:08

%S 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,

%T 72,77,87,88,104,105,106,120,127,141,150,151,159,179,189,190,225,226,

%U 241,262,271,272,277,291,312,339,360,361,375,403,423,458,468,469

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

%H Alois P. Heinz, <a href="/A153730/b153730.txt">Table of n, a(n) for n = 1..5000</a>

%p with(numtheory):

%p b:= proc(n) option remember; `if`(n=1, 1,

%p       add(b(n/q*`if`(q=2, 1, prevprime(q))), q=factorset(n)))

%p     end:

%p a:= proc(n) a(n):= b(n)+ `if`(n=1, 0, a(n-1)) end:

%p seq(a(n), n=1..100);  # _Alois P. Heinz_, Aug 09 2012

%t b[n_] := b[n] = If[n == 1, 1, Sum[b[n/q If[q == 2, 1, NextPrime[q, -1]]], {q, FactorInteger[n][[All, 1]]}]];

%t a[n_] := a[n] = b[n] + If[n == 1, 0, a[n - 1]];

%t Array[a, 100] (* _Jean-François Alcover_, Nov 20 2020, after _Alois P. Heinz_ *)

%Y Cf. A153452.

%K easy,nonn

%O 1,2

%A _Naohiro Nomoto_, Dec 31 2008

%E More terms from _Alois P. Heinz_, Aug 09 2012