A333785 Numbers m such that the average path sum is an integer when iterating from m to 1 with nondeterministic map k -> k - k/p, where p is any prime factor of k.

1, 2, 3, 4, 5, 8, 14, 16, 17, 20, 25, 32, 50, 64, 68, 82, 83, 84, 100, 101, 125, 128, 162, 163, 170, 235, 243, 256, 257, 272, 289, 456, 457, 512, 548, 621, 1024, 1028, 1040, 2048, 4096, 4112, 7225, 8192, 8738, 9248, 13058, 16384, 16480, 16481, 17476, 17477, 32128, 32768, 65536, 65537, 131072, 132098, 262144, 262148, 264196

Offset

1,2

Comments

Numbers m such that A333123(m) divides A333000(m).

Positions of ones in A333003.

Links

Antti Karttunen, Table of n, a(n) for n = 1..75; all terms up to <= 2^23

Mathematica

Position[Map[Mean[Total /@ #] &, #], _?IntegerQ][[All, 1]] &@ Nest[Function[{a, n}, Append[a, Join @@ Table[Flatten@ Prepend[#, n] & /@ a[[n - n/p]], {p, FactorInteger[n][[All, 1]]}]]] @@ {#, Length@ # + 1} &, {{{1}}}, 2^10 + 1] (* Michael De Vlieger, Apr 15 2020 *)

Crossrefs

Cf. A333000, A333001, A333003, A333123.

Subsequences: A000079, A019434.

Sequence in context: A152526 A330706 A162901 * A162900 A015925 A140294

Adjacent sequences: A333782 A333783 A333784 * A333786 A333787 A333788

Keyword

nonn

Author

Antti Karttunen, Apr 06 2020

Status

approved