cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A143771 a(n) = gcd(k + n/k), where k is over all divisors of n.

This page as a plain text file.
%I A143771 #25 Mar 29 2021 14:58:42
%S A143771 2,3,4,1,6,1,8,3,2,1,12,1,14,3,8,1,18,1,20,3,2,1,24,1,2,3,4,1,30,1,32,
%T A143771 3,2,1,12,1,38,3,8,1,42,1,44,3,2,1,48,1,2,3,4,1,54,1,8,3,2,1,60,1,62,
%U A143771 3,8,1,6,1,68,3,2,1,72,1,74,3,4,1,6,1,80,3,2,1,84,1,2,3,8,1,90,1,4,3,2,1,24,1
%N A143771 a(n) = gcd(k + n/k), where k is over all divisors of n.
%C A143771 If n is the m-th composite, then a(n) = A143772(m).
%C A143771 If n is prime, then a(n) is defined as n+1, since a(n) = gcd(1+n, n+1).
%H A143771 Antti Karttunen, <a href="/A143771/b143771.txt">Table of n, a(n) for n = 1..16384</a> (terms 2..10000 from Michael De Vlieger)
%e A143771 a(1) = gcd(1+1) = 2, i.e., the greatest common divisor of a singular set [2].
%e A143771 a(9) = gcd(1+9, 3+3, 9+1) = 2.
%e A143771 a(20) = gcd(1+20, 2+10, 4+5, 5+4, 10+2, 20+1) = 3.
%e A143771 a(44) = gcd(1+44, 2+22, 4+11, 11+4, 22+2, 44+1) = 3.
%p A143771 A143771 := proc(n) local dvs ; dvs := convert(numtheory[divisors](n),list) ; igcd(seq( op(i,dvs)+n/op(i,dvs), i=1..nops(dvs))) ; end: for n from 2 to 140 do printf("%d,",A143771(n)) ; od: # _R. J. Mathar_, Sep 05 2008
%t A143771 Table[GCD @@ Map[# + n/# &, Divisors@ n], {n, 2, 96}] (* _Michael De Vlieger_, Oct 30 2017 *)
%o A143771 (PARI) a(n) = my(d = divisors(n)); gcd(vector(#d, k, d[k]+n/d[k])); \\ _Michel Marcus_, Oct 05 2015
%Y A143771 Cf. A143772, A339873, A339914, A342918 [= (1+n) / a(n)].
%Y A143771 After n=1 differs from A342915 for the first time at n=44, where a(44) = 3, while A342915(44) = 9.
%K A143771 nonn
%O A143771 1,1
%A A143771 _Leroy Quet_, Aug 31 2008
%E A143771 Extended by _R. J. Mathar_, Sep 05 2008
%E A143771 Term a(1) = 2 prepended and Example-section extended by _Antti Karttunen_, Mar 29 2021