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

1,2

Comments

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

Links

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

Formula

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A000290, A018252, A023890.

Sequence in context: A321617 A254031 A074480 * A210503 A037074 A107423

Adjacent sequences: A194577 A194578 A194579 * A194581 A194582 A194583

Keyword

nonn

Author

Michel Lagneau, Aug 29 2011

Status

approved