

A259124


If n is representable as x*y+x+y, with x>=y>1, then a(n) is the sum of all x's and y's in all such representations. Otherwise a(n)=0.


4



0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 5, 0, 0, 6, 6, 0, 7, 0, 7, 8, 0, 0, 17, 8, 0, 10, 9, 0, 20, 0, 10, 12, 0, 10, 34, 0, 0, 14, 23, 0, 26, 0, 13, 28, 0, 0, 43, 12, 13, 18, 15, 0, 32, 14, 29, 20, 0, 0, 67, 0, 0, 36, 32, 16, 38, 0, 19, 24, 32, 0, 76, 0, 0, 44, 21, 16, 44, 0, 57, 44
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OFFSET

1,8


COMMENTS

The sequence of numbers that never appear in a(n) begins: 1, 2, 3, 11, 27, 35, 51, 53, 79, 83, 89, 93, 117, 123, 125, 135, 143, 145.
The indices n at which a(n)=0 are in A254636.  Vincenzo Librandi, Jul 16 2015


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = Sum({d: d  n+1 and 3 <= d <= sqrt(n+1)}, d + (n+1)/d  2).  Robert Israel, Aug 05 2015


EXAMPLE

11 = 3*2 + 3 + 2, so a(11)=5.


MAPLE

f:= proc(n) local D, d;
D:= select(t > (t >= 3 and t^2 <= n+1), numtheory:divisors(n+1));
add(d + (n+1)/d  2, d = D);
end proc:
map(f, [$1..100]); # Robert Israel, Aug 05 2015


PROG

(Python)
TOP = 100
a = [0]*TOP
for y in xrange(2, TOP/2):
for x in xrange(y, TOP/2):
n = x*y + x + y
if n>=TOP: break
a[n] += x+y
print a
(PARI) a(n)=sum(y=2, sqrtint(n+1)1, my(x=(ny)/(y+1)); if(denominator(x)==1, x+y)) \\ Charles R Greathouse IV, Jun 29 2015


CROSSREFS

Cf. A254636, A255361.
Sequence in context: A189885 A151673 A005397 * A273515 A021718 A193108
Adjacent sequences: A259121 A259122 A259123 * A259125 A259126 A259127


KEYWORD

nonn


AUTHOR

Alex Ratushnyak, Jun 18 2015


STATUS

approved



