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A191905
Composite deficient numbers k such that (product of proper divisors of k) mod (sum of proper divisors of k) is a prime number.
1
4, 9, 10, 25, 33, 39, 49, 57, 91, 93, 98, 105, 111, 119, 121, 145, 155, 169, 183, 185, 187, 189, 201, 205, 209, 215, 225, 235, 237, 242, 245, 265, 289, 291, 299, 305, 327, 335, 351, 355, 361, 371, 403, 413, 415, 417, 425, 427, 437, 469, 471, 475, 485, 493, 497, 515, 527, 529, 535, 543, 549, 553
OFFSET
1,1
LINKS
MAPLE
isA191905 := proc(n) if not isA125493(n) then false; else isprime( A191906(n)) ; end if; end proc:
for n from 3 to 710 do if isA191905(n) then printf("%d, ", n) ; end if; end do: # R. J. Mathar, Jun 27 2011
MATHEMATICA
fQ[n_]:=Module[{pd=Most[Divisors[n]]}, !PerfectNumberQ[n]&&CompositeQ[n] && DivisorSigma[ 1, n]<2n&& PrimeQ[Mod[Times@@pd, Total[pd]]]] Select[Range[2, 600], fQ] (* Harvey P. Dale, Jul 14 2024 *)
CROSSREFS
KEYWORD
nonn,less
AUTHOR
EXTENSIONS
Corrected by R. J. Mathar, Jun 27 2011
STATUS
approved