The On-Line Encyclopedia of Integer Sequences (OEIS)

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A104076

If k(m) is the m-th divisor (when the divisors are ordered by size) of n, then a(n) = gcd(k(1)+k(2), k(2)+k(3), k(3)+k(4), ..., k(j-1)+k(j)), where j is the number of divisors of n.
(history; published version)

#18 by Jon E. Schoenfield at Sat Oct 26 16:26:24 EDT 2019

STATUS

editing

approved

#17 by Jon E. Schoenfield at Sat Oct 26 16:26:19 EDT 2019

NAME

If k(m) is the m-th divisor (when the divisors are ordered by size) of n, then a(n) = GCDgcd(k(1)+k(2), k(2)+k(3), k(3)+k(4), ..., k(j-1)+k(j)), where j is the number of divisors of n.

EXAMPLE

The divisors of 14 are 1,2,7,14. So a(14) = GCDgcd(1+2, 2+7, 7+14) = 3.

STATUS

approved

editing

#16 by Harvey P. Dale at Tue Dec 18 12:36:09 EST 2018

STATUS

editing

approved

#15 by Harvey P. Dale at Tue Dec 18 12:36:05 EST 2018

LINKS

Harvey P. Dale, <a href="/A104076/b104076.txt">Table of n, a(n) for n = 2..1000</a>

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approved

editing

#14 by Harvey P. Dale at Tue Dec 18 12:35:05 EST 2018

STATUS

editing

approved

#13 by Harvey P. Dale at Tue Dec 18 12:35:02 EST 2018

MATHEMATICA

Table[GCD@@(Total/@Partition[Divisors[n], 2, 1]), {n, 2, 100}] (* Harvey P. Dale, Dec 18 2018 *)

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approved

editing

#12 by Jon E. Schoenfield at Sat Aug 08 21:26:59 EDT 2015

STATUS

editing

approved

#11 by Jon E. Schoenfield at Sat Aug 08 21:26:57 EDT 2015

NAME

If k(m) is the m-th divisor (when the divisors are ordered by size) of n, then a(n) = GCD(k(1)+k(2), k(2)+k(3), k(3)+k(4), ..., k(j-1)+k(j)), where j is the number of divisors of n.

EXAMPLE

The divisors of 14 are 1,2,7,14. So a(14) = GCD(1+2, 2+7, 7+14) = 3.

MAPLE

A104076 := proc(n) local dvs ; dvs := sort(convert(numtheory[divisors](n), list)) ; igcd(seq( op(i, dvs)+op(i+1, dvs), i=1..nops(dvs)-1)) ; end: for n from 2 to 140 do printf("%d, ", A104076(n)) ; od: [From _# _R. J. Mathar_, Sep 05 2008]

EXTENSIONS

Corrected definition. - _Definition corrected by _Leroy Quet_, Sep 21 2008

STATUS

approved

editing

#10 by Charles R Greathouse IV at Wed Apr 09 10:15:59 EDT 2014

EXTENSIONS

Corrected definition. - Leroy Quet , Sep 21 2008

Discussion

Wed Apr 09

10:15

OEIS Server: https://oeis.org/edit/global/2153

#9 by Charles R Greathouse IV at Wed Apr 09 10:15:51 EDT 2014

AUTHOR

Leroy Quet , Aug 31 2008

Discussion

Wed Apr 09

10:15

OEIS Server: https://oeis.org/edit/global/2152