A333002 - OEIS

%I #11 Apr 15 2020 12:30:33

%S 1,3,6,7,12,25,39,15,43,47,69,76,115,37,198,31,48,209,304,46,302,317,

%T 432,203,71,500,344,640,901,899,1271,63,1777,179,758,736,1069,786,465,

%U 361,525,789,1090,358,860,1075,1404,506,1132,132,1042,815,1133,918,1439,965,1251,4165,5522,3026,4307,6343,1273,127

%N Numerator of the average path sum when iterating from n to 1 with nondeterministic map k -> k - k/p, where p is any prime factor of k.

%H Antti Karttunen, <a href="/A333002/b333002.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = numerator(A333000(n)/A333123(n)).

%t Map[Numerator@ Mean[Total /@ #] &, #] &@ Nest[Function[{a, n}, Append[a, Join @@ Table[Flatten@Prepend[#, n] & /@ a[[n - n/p]], {p, FactorInteger[n][[All, 1]]}]]] @@ {#, Length@ # + 1} &, {{{1}}}, 63] (* _Michael De Vlieger_, Apr 15 2020 *)

%o (PARI)

%o up_to = 20000;

%o A333002list(up_to) = { my(u=vector(up_to), v=vector(up_to)); u[1] = v[1] = 1; for(n=2,up_to, my(ps=factor(n)[, 1]~); u[n] = vecsum(apply(p -> u[n-n/p], ps)); v[n] = (u[n]*n)+vecsum(apply(p -> v[n-n/p], ps))); vector(up_to, n, numerator(v[n]/u[n])); };

%o v333002 = A333002list(up_to);

%o A333002(n) = v333002[n];

%Y See A333003 for denominator.

%Y Cf. A333000, A333001, A333123.

%K nonn,frac

%O 1,2

%A _Antti Karttunen_, Apr 06 2020