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A239686 Numbers n such that if n = a U b (where U denotes concatenation) then sigma*(a) + sigma*(b) = abs(sigma*(n) - n), where sigma*(n) is the sum of the anti-divisors of n. 1
47, 118, 205, 846, 898, 1219, 4181, 4236, 4701, 4929, 6014, 6516, 13276, 30445, 59956, 61916, 63216, 67314, 72066, 79554, 90674, 106316, 128998, 129179, 136816, 142486, 143396, 180448, 229914, 284894, 357841, 421318, 483286, 486721, 487618, 500218, 642445 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Neither a or b minor than 2 are considered because numbers 1 and 2 have no anti-divisors.

Similar to A239562 but using anti-divisors instead of divisors.

LINKS

Table of n, a(n) for n=1..37.

EXAMPLE

Anti-divisors of 4701 are 2, 6, 7, 17, 79, 119, 1343, 553, 3134 and their sum is 5260. Consider 4701 as 4 U 701. Anti-divisors of 4 is 3 and of 701 are 2, 3, 23, 61, 467 whose sum is 556. At the end we have that 5260 - 4701 = 559 = 3 + 556.

MAPLE

with(numtheory);

T:=proc(t) local w, x, y; x:=t; y:=0; while x>0 do x:=trunc(x/10); y:=y+1; od; end:

P:=proc(q) local a, b, c, d, f, g, i, j, k, n;

for n from 1 to q do b:=T(n); 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;

for i from 1 to b-1 do c:=trunc(n/10^i); d:=n-c*10^i; if c>2 and d>2 then

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

f:=sigma(2*c+1)+sigma(2*c-1)+sigma(c/2^k)*2^(k+1)-6*c-2;

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

g:=sigma(2*d+1)+sigma(2*d-1)+sigma(d/2^k)*2^(k+1)-6*d-2;

if f+g=a-n then print(n); break; fi; fi; od; od; end: P(10^9);

CROSSREFS

Cf. A066272, A066417, A239687.

Sequence in context: A255149 A255142 A114646 * A118091 A235176 A044298

Adjacent sequences:  A239683 A239684 A239685 * A239687 A239688 A239689

KEYWORD

nonn,base,hard

AUTHOR

Paolo P. Lava, Mar 24 2014

STATUS

approved

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Last modified May 18 10:09 EDT 2022. Contains 353807 sequences. (Running on oeis4.)