A073930 Numbers that are equal to the sum of their anti-divisors.

5, 8, 41, 56, 946, 5186, 6874, 8104, 17386, 27024, 84026, 167786, 2667584, 4921776, 27914146, 505235234, 3238952914, 73600829714, 455879783074, 528080296234, 673223621664, 4054397778846, 4437083907194, 4869434608274, 6904301600914, 7738291969456

Offset: 1

Author

Jason Earls, Sep 03 2002

Keywords

• nonn

Comments

See A066272 for definition of anti-divisor.

Examples

			For k=5186, the anti-divisor sum: 3+4+11+23+41+253+451+943+3457 = 5186.
		

Links

• Jon Perry, Anti-perfects, anti-amicables and other records.

Crossrefs

Cf. A066417, A192272.

Programs

PARI

sad(n) = vecsum(select(t->n%t && tA066417
isok(n) = sad(n) == n; \\ Michel Marcus, Oct 12 2019

Python

from sympy import divisors
A073930 = [n for n in range(1,10**5) if sum([2*d for d in divisors(n) if n > 2*d and n % (2*d)] + [d for d in divisors(2*n-1) if n > d >=2 and n % d] + [d for d in divisors(2*n+1) if n > d >=2 and n % d]) == n] # Chai Wah Wu, Aug 14 2014

Extensions

a(16)-a(17) from Lior Manor, Mar 03 2004

a(18) from Donovan Johnson, Jun 19 2010

a(19)-a(21) by Jud McCranie, Aug 31 2019

a(22)-a(26) by Jud McCranie, Oct 10 2019