

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).


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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,...  JuriStepan 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], dsn]]; 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: A063590 A128806 A139596 * A345332 A183023 A284246
Adjacent sequences: A192032 A192033 A192034 * A192036 A192037 A192038


KEYWORD

nonn


AUTHOR

JuriStepan Gerasimov, Jun 21 2011


EXTENSIONS

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


STATUS

approved



