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A143771 a(n) = gcd(k + n/k), where k is over all divisors of n. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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).

LINKS

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

EXAMPLE

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.

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 *)

PROG

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

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.

Sequence in context: A225650 A340087 A239223 * A065331 A066262 A195989

Adjacent sequences:  A143768 A143769 A143770 * A143772 A143773 A143774

KEYWORD

nonn

AUTHOR

Leroy Quet, Aug 31 2008

EXTENSIONS

Extended by R. J. Mathar, Sep 05 2008

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

STATUS

approved

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Last modified June 13 22:55 EDT 2021. Contains 345016 sequences. (Running on oeis4.)