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A272538 Call n/m a superdivisor of n if n/m + n divides (n/m)^(n/m) + n, (n/m)^n + n/m and n^(n/m) + n/m. This sequence gives the smallest number with n superdivisors. 1
2, 1, 406, 2926, 81810, 521626, 4276350, 1590715126, 266048146 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..8.

EXAMPLE

a(0) = 2 because 2/1 + 2 does not divide (2/1)^(2/1) + 2, (2/1)^2 + 2/1, 2^(2/1) + 2/1 and 2/2 + 2 does not divide (2/2)^(2/2) + 2, (2/2)^2 + 2/2, 2^(2/2) + 2/2: 4 does not divide 6, 6, 6 and 3 does not divide 3, 2, 3.

a(0) = 2 with superdivisors {}.

a(1) = 1 with superdivisor {1}.

a(2) = 406 with superdivisors {29, 203}.

a(3) = 2926 with superdivisors {77, 209, 1463}.

a(4) = 81810 with superdivisors {405, 909, 2727, 13635}.

a(5) = 521626 with superdivisors {4921, 7049, 13727, 37259, 260813}.

a(6) = 4276350 with superdivisors {2925, 16575, 54825, 237575, 427635, 712725}.

a(7) = 1590715126 with superdivisors {607607, 939029, 4253249, 10329319, 61181351, 113622509, 795357563}.

a(8) = 266048146 with superdivisors {538559, 655291, 1000181, 1461803, 2714777, 10232621, 19003439, 133024073}.

PROG

(PARI) superdivisors(n)=select(d->Mod(d, d+n)^d==-n && Mod(d, d+n)^n==-d && Mod(n, d+n)^d==-d, divisors(n))

a(n)=my(k); while(#superdivisors(k++)!=n, ); k \\ Charles R Greathouse IV, May 06 2016

CROSSREFS

Cf. A247477, A254748.

Sequence in context: A261437 A012867 A178393 * A087037 A036109 A240234

Adjacent sequences:  A272535 A272536 A272537 * A272539 A272540 A272541

KEYWORD

nonn,more

AUTHOR

Juri-Stepan Gerasimov, Jan 19 2015

EXTENSIONS

a(4)-a(6) from Charles R Greathouse IV, Feb 19 2015.

Edited by Charles R Greathouse IV, May 06 2016

a(7)-a(8) from Charles R Greathouse IV, May 23 2016

STATUS

approved

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Last modified January 18 01:36 EST 2019. Contains 319260 sequences. (Running on oeis4.)