

A073930


Numbers that are equal to the sum of their antidivisors.


11



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
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OFFSET

1,1


COMMENTS

See A066272 for definition of antidivisor.
Subset of A192272.  Paolo P. Lava, Jan 05 2012


LINKS

Table of n, a(n) for n=1..26.
Jon Perry, Antiperfects, antiamicables and other records.


EXAMPLE

n=5186, the antidivisor 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 n1 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*n1) 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*n1), 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



