A194580 - OEIS

%I #27 Aug 25 2019 07:50:06

%S 1,15,35,143,243,323,465,899,1183,1386,1763,2065,2352,3060,3599,3612,

%T 3696,3887,5183,5358,5590,9889,10403,11663,12337,12740,12879,14329,

%U 14455,14645,16401,19043,19097,20835,22477,22499,22678,23427,25553

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

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

%H Amiram Eldar, <a href="/A194580/b194580.txt">Table of n, a(n) for n = 1..10000</a>

%F {A018252(j): A023890(A018252(j)) in A000290}. - _R. J. Mathar_, Sep 06 2011

%e 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.

%p 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:

%p for n from 1 do if issqr(A023890(A018252(n))) then  print(A018252(n)) ;  end if;

%p end do: # _R. J. Mathar_, Sep 06 2011

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

%o (PARI) isok(n) = !isprime(n) && issquare(sumdiv(n, d, d*(1-isprime(d)))); \\ _Michel Marcus_, Aug 25 2019

%Y Cf. A000290, A018252, A023890.

%K nonn

%O 1,2

%A _Michel Lagneau_, Aug 29 2011