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A239687 Numbers n such that if n = a U b (where U denotes concatenation) then abs(sigma*(a) - sigma*(b)) = abs(sigma*(n) - n), where sigma*(n) is the sum of the anti-divisors of n. 1
54, 436, 2014, 2466, 3365, 4143, 4965, 7922, 9332, 15426, 17554, 24006, 32874, 33574, 39476, 44296, 49976, 54118, 83726, 116174, 137635, 163964, 164824, 177546, 203514, 220789, 235434, 379096, 420716, 476475, 597741, 600354, 604986, 680266, 736306, 748966 (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 A239563 but using anti-divisors instead of divisors.

LINKS

Table of n, a(n) for n=1..36.

EXAMPLE

Anti-divisors of 4143 are 2, 5, 6, 1657, 2762 and their sum is 4432. Consider 4143 as 4 U 143. Anti-divisors of 4 is 3 and of 143 are 2, 3, 5, 7, 15, 19, 22, 26, 41, 57, 95 whose sum is 292. At the end we have that 4432 - 4143 = 289 = 292 - 3.

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

CROSSREFS

Cf. A066272, A066417, A239686.

Sequence in context: A232511 A262853 A230921 * A192216 A238908 A233364

Adjacent sequences:  A239684 A239685 A239686 * A239688 A239689 A239690

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, Mar 24 2014

STATUS

approved

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Last modified May 20 02:50 EDT 2019. Contains 323412 sequences. (Running on oeis4.)