A211185 - OEIS

%I #17 May 13 2013 01:54:21

%S 1,3,9,10,14,15,21,26,28,34,51,69,75,76,88,92,99,102,104,106,110,124,

%T 134,135,136,138,141,146,164,170,231,232,236,256,258,261,268,285,290,

%U 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

%N Numbers whose number of proper divisors equals the number of their anti-divisors.

%C See A066272 for definition of anti-divisor.

%C 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,...

%C 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,...

%C Numbers whose sum of proper divisors equals the sum of their anti-divisors: 1, 5, 41,...

%H Charles R Greathouse IV, <a href="/A211185/b211185.txt">Table of n, a(n) for n = 1..10000</a>

%F {n: A032741(n) = A066272(n)}.

%e 28 is here since it has 5 proper divisors {2, 4, 7, 14, 28} and 5 anti-divisors {3, 5, 8, 11, 19}.

%p for n from 1 to 700 do

%p     if A032741(n) = A066272(n) then

%p         printf("%d,",n) ;

%p     end if;

%p end do: # _R. J. Mathar_, Feb 03 2013

%o (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

%Y Cf. A000005, A032741, A066272, A073694, A178029.

%K nonn

%O 1,2

%A _Juri-Stepan Gerasimov_, Feb 02 2013

%E Entries corrected by _R. J. Mathar_, Feb 03 2013