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A194580
Nonprime numbers with a sum of nonprime divisors which is a perfect square.
1
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
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
KEYWORD
nonn
AUTHOR
Michel Lagneau, Aug 29 2011
STATUS
approved