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A073930 Numbers n such that n = sum of the anti-divisors of n. 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 (list; graph; refs; listen; history; text; internal format)
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 * A130223 A126750 A256401

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

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Last modified April 1 05:04 EDT 2020. Contains 333155 sequences. (Running on oeis4.)