A352788 Squares in A213544.

1, 9, 25, 10510564

Offset: 1

Author

Robert Israel, Apr 02 2022

Keywords

• nonn
• more

Comments

Squares that are partial sums of A023896.

Examples

			a(3) = 25 is a term because A213544(6) = 25 = 5^2.
		

Crossrefs

Cf. A000290, A023896, A213544.

Programs

Maple

s:= 1: R:= 1: count:= 1:
for n from 2 to 10^6 do
s:= s + n/2*numtheory:-phi(n);
  if issqr(s) then
     count:= count+1; R:= R, s;
  fi;
od:
R;

Mathematica

f[1] = 1; f[n_] := n*EulerPhi[n]/2; seq[len_, max_] := Module[{s = {}, sum = 0, c = 0, n = 1}, While[c < len && n < max, sum += f[n]; n++; If[IntegerQ@Sqrt[sum], c++; AppendTo[s, sum]]]; s]; seq[4, 1000] (* Amiram Eldar, Apr 07 2022 *)

Python

from itertools import count, islice
from sympy import totient
def A352788_gen(): # generator of terms
    c, m, ms = 0, 1, 1
    for n in count(1):
        c += 1 if n <= 2 else n*totient(n)//2
        if c == ms:
            yield c
        else:
            while c > ms:
                ms += 2*m+1
                m += 1
A352788_list = list(islice(A352788_gen(),4)) # Chai Wah Wu, Apr 08 2022