The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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