A192035 Numbers n with equal remainders of (product of divisors of n) mod (sum of divisors of n) and (product of proper divisors of n) mod (sum of proper divisors of n).

6, 14, 28, 51, 120, 260, 270, 496, 672, 679, 752, 924, 1260, 1320, 1540, 1960, 2055, 2262, 2651, 3808, 3948, 4381, 6413, 6435, 6944, 7900, 7980, 8010, 8128, 9809, 9945, 10242, 10920, 12690, 15456, 16830, 18018, 21728, 21970, 22320, 25296, 27930, 29190, 29792

Offset

1,1

Comments

The even perfect numbers (A000396) are a subsequence.

The deficient numbers (A005100) in the sequence are 14, 51, 679, 752, 2055, 2651, 4381, 6413, 9809, 9945, 21970,... - Juri-Stepan Gerasimov, Jul 07 2011

Links

Amiram Eldar, Table of n, a(n) for n = 1..600

Formula

{n: A187680(n)=A191906(n)}.

Example

14 is in this sequence because ((1*2*7*14) mod (1+2+7+14))=(196 mod 24)=4 and ((1*2*7) mod (1+2+7))=(14 mod 10)=4.

Mathematica

erQ[n_]:=Module[{divs=Divisors[n], ds=DivisorSigma[1, n]}, Mod[ Times@@ divs, ds] == Mod[ Times@@Most[divs], ds-n]]; Select[Range[2, 30000], erQ] (* Harvey P. Dale, Jun 13 2015 *)
Select[Range[2, 30000], Mod[(p = #^(DivisorSigma[0, #]/2)), (s = DivisorSigma[1, #])] == Mod[p/#, s - #] &] (* Amiram Eldar, Jul 21 2019 *)

Crossrefs

Cf. A001065, A007956, A187680, A191906.

Sequence in context: A349723 A128806 A139596 * A345332 A183023 A284246

Adjacent sequences: A192032 A192033 A192034 * A192036 A192037 A192038

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jun 21 2011

Extensions

Values from a(4) onwards from R. J. Mathar, Jul 05 2011

Status

approved