A072188 Numbers k that divide sigma(k-1)+sigma(k)+sigma(k+1), where sigma() is the "sum of integer divisors" function.

2, 5, 7, 33, 18336, 19262, 38184, 54722, 458010, 1402224, 1473624, 1708480, 3680560, 3733584, 5829841, 7769904, 13204262, 72873362, 136910448, 252961224, 509874800, 1138081558, 3414097921, 5440847376, 7285326504, 8986032648, 14409659936, 15953956256, 23556877704

Offset

1,1

Comments

Heuristics would seem to indicate that this sequence is infinite and sparse. Compare this sequence to the positive integers k that divide sigma(k) - the perfect and multiperfect numbers.

Links

Giovanni Resta, Table of n, a(n) for n = 1..36 (terms < 10^13)

Example

33 is in this list because sigma(32) + sigma(33) + sigma(34) = 63 + 48 + 54 = 165 = 33*5.

Prog

(PARI) for(i=2, 99999, if((sigma(i-1)+sigma(i)+sigma(i+1))%i==0, print(i)))

Crossrefs

Cf. A007691.

Sequence in context: A042931 A085394 A041875 * A277056 A160621 A028432

Adjacent sequences: A072185 A072186 A072187 * A072189 A072190 A072191

Keyword

nonn

Author

Jack Brennen, Jul 01 2002

Extensions

More terms from Jason Earls, Aug 25 2002

a(18)-a(26) from Donovan Johnson, Feb 01 2009

a(27)-a(29) from Donovan Johnson, Sep 17 2013

Status

approved