A248787 - OEIS

%I #18 Mar 18 2015 02:34:14

%S 20,26,36531,42814,4513010,63033577

%N Numbers x such that sigma(x) = rev(sigma*(x)), where sigma(x) is the sum of the divisors of x, sigma*(x) the sum of the anti-divisors of x and rev(x) the reverse of x.

%C No further terms up to 10^6.

%C a(7) > 10^10. - _Hiroaki Yamanouchi_, Mar 18 2015

%H Diana Mecum, <a href="/A130799/a130799.txt">Anti-divisors from 3 to 500</a>

%e Antidivisors of 20 are 3,8,13 and their sum is 24, while sigma(20) = 42.

%e Antidivisors of 26 are 3,4,17 and their sum is 24, while sigma(26) = 42.

%e Antidivisors of 36531 are 2, 6, 18, 22, 54, 66, 82, 162, 198, 246, 594, 738, 902, 1782, 2214, 2706, 6642, 8118, 24354 and their sum is sigma*(36531) = 48906, while sigma(36531) = 60984.

%p with(numtheory):T:=proc(w) local x,y,z; y:=w; z:=0;

%p for x from 1 to ilog10(w)+1 do z:=10*z+(y mod 10); y:=trunc(y/10); od; z; end:

%p P:=proc(q) local a,j,k,n; for n from 1 to q do

%p k:=0; j:=n; while j mod 2 <> 1 do k:=k+1; j:=j/2; od;

%p a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;

%p if T(a)=sigma(n) then print(n); fi; od; end: P(10^10);

%o (PARI) rev(n) = subst(Polrev(digits(n)), x, 10);

%o sad(n) = k=valuation(n, 2); sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;

%o isok(n) = sigma(n) == rev(sad(n)); \\ _Michel Marcus_, Dec 07 2014

%Y Cf. A000203, A066417, A178029.

%K nonn,base,more

%O 1,1

%A _Paolo P. Lava_, Oct 14 2014

%E a(5) from _Chai Wah Wu_, Dec 06 2014

%E a(6) from _Hiroaki Yamanouchi_, Mar 18 2015