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

Author

Juri-Stepan Gerasimov, Jun 19 2011

Keywords

• nonn
• less

Links

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

Crossrefs

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

Programs

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 *)

Extensions

Corrected by R. J. Mathar, Jun 27 2011