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

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Last modified December 1 23:44 EST 2022. Contains 358485 sequences. (Running on oeis4.)