This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A076495 Smallest x such that sigma(x) mod x = n, or 0 if no such x exists. 4
 2, 20, 4, 9, 0, 25, 8, 10, 15, 14, 21, 24, 27, 22, 16, 26, 39, 208, 36, 34, 51, 38, 57, 112, 95, 46, 69, 48, 115, 841, 32, 58, 45, 62, 93, 660, 155, 1369, 162, 44, 63, 1681, 50, 82, 123, 52, 129, 60, 75, 94, 72, 352, 235, 90, 329, 84, 99, 68, 265, 96, 371, 118, 64, 76 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The 0 entries are at present only conjectures. For n <= 1000, a(5) and a(898) are the only terms not found using x <= 10^11. - Donovan Johnson, Sep 20 2012 10^11 < a(898) <= 140729946996736. - Donovan Johnson, Sep 28 2013 a(898) > 10^13 and the same bound holds for a(5), if it exists. - Giovanni Resta, Apr 02 2014 LINKS Donovan Johnson, Table of n, a(n) for n = 1..1000 Carl Pomerance, On the congruences σ(n) ≡ a (mod n) and n ≡ a (mod φ(n)), Acta Arithmetica 26:3 (1974-1975), pp. 265-272. (See theorem 4.) EXAMPLE n=1: solution = smallest prime = 2. n=3: solution 4 since Mod(sigma(4),4) = Mod(7,4) = 3. n=5: Very difficult case, no solution below 10^7 (see comment by Donovan Johnson). MATHEMATICA f[x_] := s=Mod[DivisorSigma[1, n], n]; t=Table[0, {256}]; Do[s=f[n]; If[s<257&&t[[s]]==0, t[[s]]=n], {n, 1, 10000000}]; t PROG (PARI) a(n)=my(k); while(sigma(k++)%k!=n, ); k \\ Charles R Greathouse IV, Dec 28 2013 CROSSREFS Cf. A045768, A045769, A045770, A054024. Sequence in context: A082259 A077339 A077341 * A308387 A058403 A083297 Adjacent sequences:  A076492 A076493 A076494 * A076496 A076497 A076498 KEYWORD nonn AUTHOR Labos Elemer, Oct 21 2002 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 May 25 12:30 EDT 2019. Contains 323568 sequences. (Running on oeis4.)