A333002 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.

1, 3, 6, 7, 12, 25, 39, 15, 43, 47, 69, 76, 115, 37, 198, 31, 48, 209, 304, 46, 302, 317, 432, 203, 71, 500, 344, 640, 901, 899, 1271, 63, 1777, 179, 758, 736, 1069, 786, 465, 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

Offset: 1

Author

Antti Karttunen, Apr 06 2020

Keywords

• nonn
• frac

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

See A333003 for denominator.

Cf. A333000, A333001, A333123.

Programs

Mathematica

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 *)

PARI

up_to = 20000;
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])); };
v333002 = A333002list(up_to);
A333002(n) = v333002[n];

Formula

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