A272716 Numbers equal to the sum of their proper divisors d such that d mod 3 = 1.

440, 28109312, 79228362752

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