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

Author

Antti Karttunen, Apr 06 2020

Keywords

• nonn

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

Crossrefs

Cf. A333000, A333001, A333003, A333123.

Subsequences: A000079, A019434.

Programs

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 *)