A248787 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.

20, 26, 36531, 42814, 4513010, 63033577

Offset: 1

Author

Paolo P. Lava, Oct 14 2014

Keywords

• nonn
• base
• more

Comments

No further terms up to 10^6.

a(7) > 10^10. - Hiroaki Yamanouchi, Mar 18 2015

Examples

			Antidivisors of 20 are 3,8,13 and their sum is 24, while sigma(20) = 42.
Antidivisors of 26 are 3,4,17 and their sum is 24, while sigma(26) = 42.
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.
		

Links

• Diana Mecum, Anti-divisors from 3 to 500

Crossrefs

Cf. A000203, A066417, A178029.

Programs

Maple

with(numtheory):T:=proc(w) local x,y,z; y:=w; z:=0;
for x from 1 to ilog10(w)+1 do z:=10*z+(y mod 10); y:=trunc(y/10); od; z; end:
P:=proc(q) local a,j,k,n; for n from 1 to q do
k:=0; j:=n; while j mod 2 <> 1 do k:=k+1; j:=j/2; od;
a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;
if T(a)=sigma(n) then print(n); fi; od; end: P(10^10);

PARI

rev(n) = subst(Polrev(digits(n)), x, 10);
sad(n) = k=valuation(n, 2); sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;
isok(n) = sigma(n) == rev(sad(n)); \\ Michel Marcus, Dec 07 2014

Extensions

a(5) from Chai Wah Wu, Dec 06 2014

a(6) from Hiroaki Yamanouchi, Mar 18 2015