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

1,2

Links

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

Formula

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

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 *)

Prog

(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];

Crossrefs

See A333003 for denominator.

Cf. A333000, A333001, A333123.

Sequence in context: A190118 A249714 A250177 * A333000 A175048 A294231

Adjacent sequences: A332999 A333000 A333001 * A333003 A333004 A333005

Keyword

nonn,frac

Author

Antti Karttunen, Apr 06 2020

Status

approved