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 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 (list; graph; refs; listen; history; text; internal format)
 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 MATHEMATICA a[n_] := Sum[Boole[3 <= d <= Sqrt[n+1]] (d+(n+1)/d-2), {d, Divisors[n+1]}]; Array[a, 100] (* Jean-François Alcover, Jun 08 2020, after Maple *) PROG (Python) TOP = 100 a = *TOP for y in range(2, TOP//2):   for x in range(y, TOP//2):     n = x*y + x + y     if n>=TOP: break     a[n] += x+y print(a[1:]) (PARI) a(n)=sum(y=2, sqrtint(n+1)-1, my(x=(n-y)/(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 A308225 A021718 Adjacent sequences:  A259121 A259122 A259123 * A259125 A259126 A259127 KEYWORD nonn AUTHOR Alex Ratushnyak, Jun 18 2015 STATUS approved

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Last modified January 26 05:13 EST 2022. Contains 350572 sequences. (Running on oeis4.)