login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A211185
Numbers whose number of proper divisors equals the number of their anti-divisors.
1
1, 3, 9, 10, 14, 15, 21, 26, 28, 34, 51, 69, 75, 76, 88, 92, 99, 102, 104, 106, 110, 124, 134, 135, 136, 138, 141, 146, 164, 170, 231, 232, 236, 256, 258, 261, 268, 285, 290, 309, 321, 328, 386, 394, 405, 411, 424, 429, 441, 484, 490, 525, 531, 574, 580, 590, 602, 608, 614, 615, 620, 628, 639, 645, 651, 656, 658
OFFSET
1,2
COMMENTS
See A066272 for definition of anti-divisor.
Numbers of divisors of n such that number of proper divisors of n equals the number of anti-divisors of n: 1, 2, 2, 3, 4, 4, 4, 4, 6, 4, 4, 4, 6, 6, 4, 4, 4, 12, 4, 6, 10, 4, 8, 8, 4, 12, 4, 6, 4, 12, 4, 4, 4,...
Primes p such that number of proper divisors of p - 1 equals the number of anti-divisors of p - 1 and number of proper divisors of p + 1 equals the number of anti-divisors of p + 1 : 2, 103, 137, 257,...
Numbers whose sum of proper divisors equals the sum of their anti-divisors: 1, 5, 41,...
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
{n: A032741(n) = A066272(n)}.
EXAMPLE
28 is here since it has 5 proper divisors {2, 4, 7, 14, 28} and 5 anti-divisors {3, 5, 8, 11, 19}.
MAPLE
for n from 1 to 700 do
if A032741(n) = A066272(n) then
printf("%d, ", n) ;
end if;
end do: # R. J. Mathar, Feb 03 2013
PROG
(PARI) is(n)=numdiv(2*n+1)+numdiv(2*n-1)+numdiv(n>>valuation(n, 2))-numdiv(n)==4 || n==1 \\ Charles R Greathouse IV, Feb 04 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Entries corrected by R. J. Mathar, Feb 03 2013
STATUS
approved