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

Author

Amiram Eldar, May 12 2020

Keywords

• nonn
• more

Comments

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

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

Examples

			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.
		

Crossrefs

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

Programs

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