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

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

A. Karttunen, Scheme-program for computing this sequence.

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A106490-A106491.

Sequence in context: A345310 A029908 A081758 * A338038 A112264 A118503

Adjacent sequences: A106489 A106490 A106491 * A106493 A106494 A106495

Keyword

nonn

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.

Status

approved