A334816 Least number that reaches 1 after n iterations of the map k -> usigma(k)/ud(k) if ud(k) | usigma(k), and k -> 1 otherwise, where ud(k) is the number of unitary divisors of k (A034444) and usigma(k) is their sum (A034448).

1, 2, 3, 5, 9, 17, 43, 137, 281, 673, 2401, 4801, 9601, 170761, 341521, 683041, 5114881, 31846081, 131955841, 1985902081, 7545868801

Offset

0,2

Comments

Apparently, all the terms are primes or powers of primes.

a(21) > 10^10, if it exists.

Links

Table of n, a(n) for n=0..20.

Example

a(3) = 5 since usigma(5)/ud(5) = 6/2 = 3, usigma(3)/ud(3) = 4/2 = 2, and usigma(2)/ud(2) = 3/2 is not an integer, hence there are 3 iterations: 5 -> 3 -> 2 -> 1, and 5 is the least number with 3 iterations.

Mathematica

usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); ud[n_] := 2^PrimeNu[n]; rat[n_] := If[IntegerQ[r = usigma[n]/ud[n]], r, 1]; f[n_] := Length @ FixedPointList[rat, n] - 1; max = 10; seq = Table[0, {max}]; c = 0; n = 1; While[c < max, i = f[n]; If[i <= max && seq[[i]] == 0, c++; seq[[i]] = n]; n++]; seq

Crossrefs

Cf. A034444, A034448, A103826, A103827, A330814, A330815.

Sequence in context: A341960 A137155 A014227 * A064769 A320641 A365640

Adjacent sequences: A334813 A334814 A334815 * A334817 A334818 A334819

Keyword

nonn,more

Author

Amiram Eldar, May 12 2020

Status

approved