OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
William D. Banks, Florian Luca, Filip Saidak, and Igor E. Shparlinski, Values of arithmetical functions equal to a sum of two squares, Quarterly Journal of Mathematics, Vol. 56, No. 2 (2005), pp. 123-139, alternative link.
FORMULA
c1 * x/log(x)^(3/2) < N(x) < c2 * x/log(x)^(3/2), where N(x) is the number of terms <= x, and c1 and c2 are two positive constants (Banks et al., 2005).
EXAMPLE
1 is a term since psi(1) = 1 = 0^2 + 1^2.
MATHEMATICA
psi[1] = 1; psi[n_] := n * Times @@ (1 + 1/Transpose[FactorInteger[n]][[1]]); Select[Range[200], SquaresR[2, psi[#]] > 0 &]
PROG
(Python)
from itertools import count, islice
from collections import Counter
from sympy import factorint
def A333910_gen(): # generator of terms
return filter(lambda n:all(p & 3 != 3 or e & 1 == 0 for p, e in sum((Counter(factorint(1+p))+Counter({p:e-1}) for p , e in factorint(n).items()), start=Counter()).items()), count(1))
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Apr 09 2020
STATUS
approved