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

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, 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, 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

Offset: 1

Author

Leroy Quet, Aug 31 2008

Keywords

• nonn

Comments

If n is the m-th composite, then a(n) = A143772(m).

If n is prime, then a(n) is defined as n+1, since a(n) = gcd(1+n, n+1).

Examples

			a(1) = gcd(1+1) = 2, i.e., the greatest common divisor of a singular set [2].
a(9) = gcd(1+9, 3+3, 9+1) = 2.
a(20) = gcd(1+20, 2+10, 4+5, 5+4, 10+2, 20+1) = 3.
a(44) = gcd(1+44, 2+22, 4+11, 11+4, 22+2, 44+1) = 3.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384 (terms 2..10000 from Michael De Vlieger)

Crossrefs

Cf. A143772, A339873, A339914, A342918 [= (1+n) / a(n)].

After n=1 differs from A342915 for the first time at n=44, where a(44) = 3, while A342915(44) = 9.

Programs

Maple

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

Mathematica

Table[GCD @@ Map[# + n/# &, Divisors@ n], {n, 2, 96}] (* Michael De Vlieger, Oct 30 2017 *)

PARI

a(n) = my(d = divisors(n)); gcd(vector(#d, k, d[k]+n/d[k])); \\ Michel Marcus, Oct 05 2015

Extensions

Extended by R. J. Mathar, Sep 05 2008

Term a(1) = 2 prepended and Example-section extended by Antti Karttunen, Mar 29 2021