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

440, 28109312, 79228362752

Offset: 1

Author

Giovanni Resta, May 05 2016

Keywords

• nonn
• bref
• more
• hard

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.

Examples

			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.
		

Crossrefs

Cf. A272715, A000396.

Programs

Mathematica

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

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