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Numbers k that divide sigma(k-1)+sigma(k)+sigma(k+1), where sigma() is the "sum of integer divisors" function.
3

%I #18 Aug 20 2021 22:49:25

%S 2,5,7,33,18336,19262,38184,54722,458010,1402224,1473624,1708480,

%T 3680560,3733584,5829841,7769904,13204262,72873362,136910448,

%U 252961224,509874800,1138081558,3414097921,5440847376,7285326504,8986032648,14409659936,15953956256,23556877704

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

%C 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.

%H Giovanni Resta, <a href="/A072188/b072188.txt">Table of n, a(n) for n = 1..36</a> (terms < 10^13)

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

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

%Y Cf. A007691.

%K nonn

%O 1,1

%A _Jack Brennen_, Jul 01 2002

%E More terms from _Jason Earls_, Aug 25 2002

%E a(18)-a(26) from _Donovan Johnson_, Feb 01 2009

%E a(27)-a(29) from _Donovan Johnson_, Sep 17 2013