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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

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Last modified May 25 12:30 EDT 2019. Contains 323568 sequences. (Running on oeis4.)