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%I #10 Dec 12 2023 17:58:26
%S 0,2,3,2,5,5,7,2,3,7,2,5,4,9,8,2,8,5,10,7,10,4,5,5,5,6,3,9,11,10,4,2,
%T 5,10,12,5,10,12,7,7,5,12,7,4,8,7,11,5,7,7,11,6,8,5,7,9,13,13,14,10,7,
%U 6,10,2,9,7,13,10,8,14,8,5,10,12,8,12,9,9,16,7,3,7,11,12,13,9,14,4,17,10
%N Sum of digits of all distinct prime factors of n.
%H Michael S. Branicky, <a href="/A095402/b095402.txt">Table of n, a(n) for n = 1..10000</a>
%e n = 1000: prime set = {2, 5}, a[1000] = 7;
%e n = 255255: prime set={3, 5, 7, 11, 13, 17}, a[255255]= 3+5+7+2+4+8 = 29.
%t ffi[x_] :=Flatten[FactorInteger[x]] lf[x_] :=Length[FactorInteger[x]] ba[x_] :=Table[Part[ffi[x], 2*j-1], {j, 1, lf[x]}] sd[x_] :=Apply[Plus, IntegerDigits[x]] tdp[x_] :=Flatten[Table[IntegerDigits[Part[ba[x], j]], {j, 1, lf[x]}], 1] sdp[x_] :=Apply[Plus, tdp[x]] Table[sdp[w], {w, 1, 150}]
%t Table[Total[Flatten[IntegerDigits[First/@FactorInteger[n]]]],{n,1,100}] (Zak Seidov)
%o (Python)
%o from sympy import factorint
%o def a(n): return sum(sum(map(int, str(p))) for p in factorint(n))
%o print([a(n) for n in range(1, 91)]) # _Michael S. Branicky_, Dec 12 2023
%Y Cf. A007953, A051351, A141346.
%K nonn,base
%O 1,2
%A _Labos Elemer_, Jun 21 2004
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