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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,... - 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: A063590 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

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Last modified December 6 20:22 EST 2021. Contains 349567 sequences. (Running on oeis4.)