A191905 Composite deficient numbers k such that (product of proper divisors of k) mod (sum of proper divisors of k) is a prime number.

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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Cf. A001065, A005100, A007956, A125493, A191906.

Sequence in context: A077584 A093896 A332449 * A113432 A129830 A113434

Adjacent sequences: A191902 A191903 A191904 * A191906 A191907 A191908

Keyword

nonn,less

Author

Juri-Stepan Gerasimov, Jun 19 2011

Extensions

Corrected by R. J. Mathar, Jun 27 2011

Status

approved