A274028 Numbers whose sum of divisors and sum of anti-divisors are both palindromes.

1, 2, 3, 4, 5, 208, 211, 489, 39765, 41689, 43545, 45772, 1226372, 2028209, 3131006, 5639781, 45224913, 402664481, 509561899, 534611505, 30392347941, 37824872279, 42100531202, 67332408085, 208185050013, 363340615629, 1316050604902, 1792459658755, 2465601425469

Offset: 1

Author

Paolo P. Lava, Jun 07 2016

Keywords

• nonn
• base

Comments

Intersection of A028980 and A274049. - Michel Marcus, Jun 08 2016

Examples

			Anti-divisors of 208 are 3, 5, 32, 83, 139 and their sum is 262 ; sigma(208) = 434.
		

Crossrefs

Cf. A000203, A002113, A028980, A066417, A073956, A274049.

Programs

Maple

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

Extensions

Missing a(1)-a(2) and a(17)-a(20) from Giovanni Resta, Jun 19 2016

a(21)-a(29) from Max Alekseyev, Jan 28 2024