A377539 The number of iterations of the map x -> x + A000005(x), starting from n, until reaching an even number, and always at least one iteration taken.

1, 1, 4, 3, 3, 1, 2, 1, 1, 1, 6, 1, 5, 1, 4, 3, 4, 1, 3, 1, 2, 1, 2, 1, 1, 1, 16, 1, 16, 1, 15, 1, 14, 1, 13, 11, 13, 1, 12, 1, 12, 1, 11, 1, 10, 1, 2, 1, 1, 1, 9, 1, 9, 1, 8, 1, 7, 1, 7, 1, 6, 1, 5, 5, 5, 1, 5, 1, 4, 1, 4, 1, 3, 1, 2, 1, 2, 1, 2, 1, 1, 1, 38, 1, 37, 1, 36, 1, 36, 1, 35, 1, 35

Offset

1,3

Comments

The iteration step is x -> A062249(x).

a(n) = 1 if and only if n is an odd square or an even nonsquare. - Robert Israel, Oct 31 2024

Links

Table of n, a(n) for n=1..93.

Example

For n = 2, there is a(2) = 1 iteration to an even number: 2 -> 4 (with at least one iteration so 2 itself is not the even number target).
For n = 3 there are a(3) = 4 iterations to reach an even number: 3 -> 5 -> 7 -> 9 -> 12.

Maple

f:= proc(n) local x, i;
  x:= n;
  for i from 1 do x:= x + numtheory:-tau(x); if x::even then return i fi od
end proc:
map(f, [$1..200]); # Robert Israel, Oct 31 2024

Mathematica

a[n_] := -1 + Length@ NestWhileList[# + DivisorSigma[0, #] &, n, OddQ, {2, 1}]; Array[a, 100] (* Amiram Eldar, Oct 31 2024 *)

Crossrefs

Cf. A000005, A062249 (step), A064491 (trajectory of 1).

Sequence in context: A016699 A060373 A090280 * A177158 A177034 A177933

Adjacent sequences: A377536 A377537 A377538 * A377540 A377541 A377542

Keyword

nonn,look

Author

Ctibor O. Zizka, Oct 31 2024

Status

approved