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A274028
Numbers whose sum of divisors and sum of anti-divisors are both palindromes.
1
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
1,2
COMMENTS
Intersection of A028980 and A274049. - Michel Marcus, Jun 08 2016
EXAMPLE
Anti-divisors of 208 are 3, 5, 32, 83, 139 and their sum is 262 ; sigma(208) = 434.
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);
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Jun 07 2016
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
STATUS
approved