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

%I A106492 #21 Jul 09 2025 04:25:12
%S A106492 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,
%T A106492 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,
%U A106492 16,12,22,31,59,12,61,33,12,7,18,16,67,21,26,14,71,10,73,39,10,23,18
%N A106492 Total sum of bases and exponents in Quetian Superfactorization of n, excluding the unity-exponents at the tips of branches.
%H A106492 Alois P. Heinz, <a href="/A106492/b106492.txt">Table of n, a(n) for n = 1..10000</a>
%H A106492 A. Karttunen, <a href="/A091247/a091247.scm.txt">Scheme-program for computing this sequence.</a>
%F A106492 Additive with a(p^e) = p + a(e).
%e A106492 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.
%p A106492 a:= proc(n) option remember;
%p A106492       add(i[1]+a(i[2]), i=ifactors(n)[2])
%p A106492     end:
%p A106492 seq(a(n), n=1..100);  # _Alois P. Heinz_, Nov 06 2014
%t A106492 a[1] = 0; a[n_] := a[n] = #[[1]] + a[#[[2]]]& /@ FactorInteger[n] // Total; Array[a, 100] (* _Jean-François Alcover_, Mar 03 2016 *)
%Y A106492 Cf. A106490-A106491.
%K A106492 nonn
%O A106492 1,2
%A A106492 _Antti Karttunen_, May 09 2005 based on _Leroy Quet_'s message ('Super-Factoring' An Integer) posted to SeqFan-mailing list on Dec 06 2003