A272715 Numbers equal to the sum of their proper divisors d such that d mod 3 = 2.

280, 34960, 4960000, 15887872, 20527600, 105056320, 44781248512

Offset

1,1

Comments

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..7.

Example

The proper divisors of 280 which are congruent to 2 mod 3 are 2, 5, 8, 14, 20, 35, 56, and 140. Since their sum is 280, 280 is a term.

Mathematica

Select[Range[40000], # == Plus @@ Select[ Most@ Divisors[#], Mod[#, 3] == 2 &] &]

Prog

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

Crossrefs

Cf. A272716, A000396, A078182 (sum of proper and improver divisors).

Sequence in context: A094895 A223107 A218411 * A282439 A255498 A091034

Adjacent sequences: A272712 A272713 A272714 * A272716 A272717 A272718

Keyword

nonn,more

Author

Giovanni Resta, May 05 2016

Status

approved