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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. 1
20, 26, 36531, 42814, 4513010, 63033577 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
No further terms up to 10^6.
a(7) > 10^10. - Hiroaki Yamanouchi, Mar 18 2015
LINKS
EXAMPLE
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.
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);
PROG
(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
CROSSREFS
Sequence in context: A101070 A219805 A219456 * A070717 A114813 A069827
KEYWORD
nonn,base,more
AUTHOR
Paolo P. Lava, Oct 14 2014
EXTENSIONS
a(5) from Chai Wah Wu, Dec 06 2014
a(6) from Hiroaki Yamanouchi, Mar 18 2015
STATUS
approved

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Last modified March 19 02:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)