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

Author

Jack Brennen, Jul 01 2002

Keywords

• nonn

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.

Examples

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

Links

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

Crossrefs

Cf. A007691.

Programs

PARI

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

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