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A082772 Integers n such that there exists at least one divisor d of n, 1 < d < n, such that d divides n and d+1 divides n+1. 2

%I

%S 8,14,15,20,24,26,27,32,35,38,39,44,48,50,51,56,62,63,64,65,68,74,75,

%T 80,84,86,87,90,92,95,98,99,104,110,111,116,119,120,122,123,124,125,

%U 128,132,134,135,140,143,144,146,147,152,155,158,159,164,168,170,171,174

%N Integers n such that there exists at least one divisor d of n, 1 < d < n, such that d divides n and d+1 divides n+1.

%H Amiram Eldar, <a href="/A082772/b082772.txt">Table of n, a(n) for n = 1..10000</a>

%e 24 is a term since 4 divides 24 and 5 divides 25.

%t aQ[n_] := AnyTrue[Most @ Rest @ Divisors[n], Divisible[n+1, #+1] &]; Select[ Range[2, 200], aQ ] (* _Amiram Eldar_, Sep 18 2019 *)

%o (C++) for (int a = 1; a < 200; a++) for (int b = 2; b < a; b++) if ((a%b==0)&&((a+1)%(b+1)==0)) cout << a << ", "; // outputs a

%o (PARI) isok(n) = {fordiv(n, d, if ((d>1) && (d<n) && ! ((n+1) % (d+1)), return (1)););} \\ _Michel Marcus_, Sep 18 2019

%K easy,nonn

%O 1,1

%A Anne M. Donovan (anned3005(AT)aol.com), May 21 2003

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Last modified February 25 22:37 EST 2021. Contains 341618 sequences. (Running on oeis4.)