A215113 a(n) is the number of different prime divisors of A214723(n).

1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 3, 2, 3, 1, 2, 2, 2, 2, 3, 1, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3, 2, 2, 2, 2, 2, 3, 1, 3, 3, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 3

Offset: 1

Author

Vladimir Shevelev, Aug 03 2012

Keywords

• nonn

Comments

The records of a(n) are a(1)=1, a(3)=2, a(12)=3, a(132)=4,... Is the sequence unbounded?

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A001221, A214723.

Programs

Mathematica

nn = 2000; ps = Prime[Range[PrimePi[Sqrt[nn]]]]; t = Flatten[Table[ ps[[i]]^2 + ps[[j]]^2, {i, Length[ps]}, {j, i, Length[ps]}]]; t =
Select[t, # <= nn &]; PrimeNu[Sort[Transpose[Select[Tally[t], #[[2]] == 1 &]][[1]]]] (* G. C. Greubel, May 16 2017 *)

Formula

a(n) = A001221(A214723(n)). - Michel Marcus, Feb 08 2016