A106492 Total sum of bases and exponents in Quetian Superfactorization of n, excluding the unity-exponents at the tips of branches.

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

Offset: 1

Author

Antti Karttunen, May 09 2005 based on Leroy Quet's message ('Super-Factoring' An Integer) posted to SeqFan-mailing list on Dec 06 2003

Keywords

• nonn

Examples

			a(64) = 7, as 64 = 2^6 = 2^(2^1*3^1) and 2+2+3=7. Similarly, for 360 = 2^(3^1) * 3^(2^1) * 5^1 we get a(360) = 2+3+3+2+5 = 15. See comments at A106490.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• A. Karttunen, Scheme-program for computing this sequence.

Crossrefs

Cf. A106490-A106491.

Programs

Maple

a:= proc(n) option remember;
      add(i[1]+a(i[2]), i=ifactors(n)[2])
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Nov 06 2014

Mathematica

a[1] = 0; a[n_] := a[n] = #[[1]] + a[#[[2]]]& /@ FactorInteger[n] // Total; Array[a, 100] (* Jean-François Alcover, Mar 03 2016 *)

Formula

Additive with a(p^e) = p + a(e).