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Numbers n for which A259124(n) = A259124(n-1) + 1.
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%I #23 Nov 13 2024 16:40:53

%S 20,49,2096,5684,14847,440876,18770091,40882585915,5598199195808,

%T 35959924244180

%N Numbers n for which A259124(n) = A259124(n-1) + 1.

%C Is the sequence infinite?

%C a(11) > 5 * 10^13. - _Hiroaki Yamanouchi_, Aug 24 2015

%o (Python)

%o TOP = 5000*5000

%o a = [0]*TOP

%o for y in range(2, 5000):

%o z = TOP//y + 1

%o for x in range(y, z):

%o n = x*y + x + y

%o if n>=TOP: break

%o a[n] += x+y

%o for n in range(1,TOP):

%o if a[n]==a[n-1]+1 and a[n]>0: print(n, end=', ')

%o (PARI) a259124(n)=sum(y=2, sqrtint(n+1)-1, my(x=(n-y)/(y+1)); if(denominator(x)==1, x+y));

%o isok(n)= a259124(n) == a259124(n-1) + 1; \\ _Michel Marcus_, Aug 05 2015

%Y Cf. A259124, A259432.

%K nonn,more

%O 1,1

%A _Alex Ratushnyak_, Jul 15 2015

%E a(8)-a(9) from _Hiroaki Yamanouchi_, Aug 24 2015

%E a(10) from _Hiroaki Yamanouchi_, Aug 25 2015