

A272716


Numbers equal to the sum of their proper divisors d such that d mod 3 = 1.


2




OFFSET

1,1


COMMENTS

10^11 < a(4) <= 8581256320000.
The numbers equal to the sum of their proper divisors which are a multiple of 3 are the perfect numbers (A000396) multiplied by 3.


LINKS

Table of n, a(n) for n=1..3.


EXAMPLE

The proper divisors of 440 which are congruent to 1 mod 3 are 1, 4, 10, 22, 40, 55, 88, and 220. Since their sum is 440, 440 is a term.


MATHEMATICA

Select[Range[5000], # == Plus @@ Select[Most@ Divisors@#, Mod[#, 3] == 1 &] &]


PROG

(PARI) is(n)=sumdiv(n, d, if(d%3==1, d, 0))==if(n%3==1, 2*n, n) \\ Charles R Greathouse IV, May 09 2016


CROSSREFS

Cf. A272715, A000396.
Sequence in context: A234202 A061626 A187239 * A124170 A252193 A207650
Adjacent sequences: A272713 A272714 A272715 * A272717 A272718 A272719


KEYWORD

nonn,bref,more,hard


AUTHOR

Giovanni Resta, May 05 2016


STATUS

approved



