A286917 Numbers k such that there is an anti-divisor d of k satisfying sigma(d) = k.

3, 4, 13, 32, 40, 60, 121, 364, 1093, 3200, 3280, 9841, 15120, 16380, 29282, 29524, 88573, 91728, 264992, 265720, 797161, 2391484, 7174453, 21523360, 40098240, 64570081, 71495424, 78427440, 193690562, 193710244, 229909120, 581130733, 689727360, 1743392200, 5230176601

Offset

1,1

Comments

As powers of 3 are in the sequence (larger than 1), the sequence is infinite. - David A. Corneth, Jul 20 2020

Links

Table of n, a(n) for n=1..35.

Formula

sigma(3^m) is in the sequence, as is sigma(3^m*(3^(m + 1) - 2)) for prime 3^(m + 1) - 2. - David A. Corneth, Jul 20 2020

Example

Anti-divisors of 60 are 7, 8, 11, 17, 24, 40 and sigma(24) = 60.

Maple

with(numtheory): P:= proc(q) local a, k, n; for n from 3 to q do a:=[];
for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then a:=[op(a), k]; fi; od;
for k from 1 to nops(a) do if n=sigma(a[k]) then print(n); break; fi; od;
od; end: P(10^4); # Paolo P. Lava, May 16 2017

Prog

(PARI) isok(n) = {ad = select(t->n%t && t<n, concat(concat(divisors(2*n-1), divisors(2*n+1)), 2*divisors(n))); for (k=1, #ad, if ((n % ad[k]) && (sigma(ad[k])== n), return (1)); ); } \\ Michel Marcus, May 20 2017

Crossrefs

Cf. A000203, A014224, A066272, A081756, A130799.

Sequence in context: A192872 A036672 A174684 * A084315 A194649 A062165

Adjacent sequences: A286914 A286915 A286916 * A286918 A286919 A286920

Keyword

nonn

Author

Paolo P. Lava, May 16 2017

Extensions

More terms from Michel Marcus, May 20 2017

a(22)-a(26) from Jinyuan Wang, Jul 20 2020

a(27)-a(35) from David A. Corneth, Jul 20 2020

Status

approved