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

1,1

Comments

See A066272 for definition of anti-divisor.

Subset of A192272. - Paolo P. Lava, Jan 05 2012

Links

Table of n, a(n) for n=1..26.

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

Example

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

Maple

A073930:= proc(q) local a, k, n;
for n from 1 to q do
a:=0; for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then a:=a+k; fi;
od; if a=n then print(n); fi; od; end:
A073930(10^10); # Paolo P. Lava, Mar 11 2013

Prog

(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
(PARI) sad(n) = vecsum(select(t->n%t && t<n, concat(concat(divisors(2*n-1), divisors(2*n+1)), 2*divisors(n)))); \\ A066417
isok(n) = sad(n) == n; \\ Michel Marcus, Oct 12 2019

Crossrefs

Cf. A066417, A192272.

Sequence in context: A298935 A258786 A192272 * A342021 A130223 A126750

Adjacent sequences: A073927 A073928 A073929 * A073931 A073932 A073933

Keyword

nonn,more

Author

Jason Earls, Sep 03 2002

Extensions

Two more terms 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

Status

approved