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%I #15 Jan 15 2015 10:12:13
%S 0,2,5,3,8,5,12,10,7,2,13,10,23,16,11,9,26,23,4,9,2,13,36,33,28,15,12,
%T 5,34,29,60,58,47,30,23,20,57,38,25,20,61,54,11,0,5,28,75,72,65,60,43,
%U 30,83,80,69,62,43,14,73,68,7,38,31,29,16,5,72,55,32,25
%N a(1)= 0; for n > 1, a(n) = a(n-1) - P(n) if that number is zero or positive, otherwise a(n)= a(n-1)+ P(n), where P(n) is the largest prime factor of n (A006530).
%C a(n) = 0 for n = 1, 44, 125, 373, 1123, 1353, 5071, 19577, …
%H Michel Lagneau, <a href="/A185112/b185112.txt">Table of n, a(n) for n = 1..5000</a>
%p with(numtheory):a0:=0:for n from 2 to 100 do: x:=factorset(n):n1:=nops(x): p:=x[n1]:a1:=a0-p:if a1< 0 then a1:=a0+p:else fi: printf(`%d, `,a1): a0:=a1: od:
%t nxt[{n_,a_}]:=Module[{lpf=FactorInteger[n+1][[-1,1]]},{n+1,If[ a-lpf> = 0,a-lpf,a+lpf]}]; Transpose[NestList[nxt,{1,0},70]][[2]] (* _Harvey P. Dale_, Jan 15 2015 *)
%Y Cf. A006530.
%K nonn
%O 1,2
%A _Michel Lagneau_, Jan 23 2012
%E Definition modified by _Harvey P. Dale_, Jan 15 2015
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