A194580 Nonprime numbers with a sum of nonprime divisors which is a perfect square.

1, 15, 35, 143, 243, 323, 465, 899, 1183, 1386, 1763, 2065, 2352, 3060, 3599, 3612, 3696, 3887, 5183, 5358, 5590, 9889, 10403, 11663, 12337, 12740, 12879, 14329, 14455, 14645, 16401, 19043, 19097, 20835, 22477, 22499, 22678, 23427, 25553

Offset: 1

Author

Michel Lagneau, Aug 29 2011

Keywords

• nonn

Comments

If n is prime, the sum is equal to 1.

Examples

			The divisors of 465 are {1, 3, 5, 15, 31, 93, 155, 465} and the sum of the nonprime divisors 1 + 15 + 93 + 155 + 465 = 729 = 27^2, hence 465 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000290, A018252, A023890.

Programs

Maple

A023890 := proc(n) a := 0 ; for d in numtheory[divisors](n) do if not isprime(d) then a := a+d; end if; end do; a; end proc:
for n from 1 do if issqr(A023890(A018252(n))) then  print(A018252(n)) ;  end if;
end do: # R. J. Mathar, Sep 06 2011

Mathematica

f[n_] := IntegerQ[Sqrt[Total[Select[Divisors[n], ! PrimeQ[#] &]]]]; Select[Range[25553], ! PrimeQ[#] && f[#] &] (* T. D. Noe, Sep 06 2011 *)

PARI

isok(n) = !isprime(n) && issquare(sumdiv(n, d, d*(1-isprime(d)))); \\ Michel Marcus, Aug 25 2019

Formula

{A018252(j): A023890(A018252(j)) in A000290}. - R. J. Mathar, Sep 06 2011