A058075 -id:A058075 - cp's OEIS frontend

A060780 a(n) = gcd(sigma(n+1), sigma(n)), where sigma = A000203.

1, 1, 1, 1, 6, 4, 1, 1, 1, 6, 4, 14, 2, 24, 1, 1, 3, 1, 2, 2, 4, 12, 12, 1, 1, 2, 8, 2, 6, 8, 1, 3, 6, 6, 1, 1, 2, 4, 2, 6, 6, 4, 4, 6, 6, 24, 4, 1, 3, 3, 2, 2, 6, 24, 24, 40, 10, 30, 12, 2, 2, 8, 1, 1, 12, 4, 2, 6, 48, 72, 3, 1, 2, 2, 4, 4, 24, 8, 2, 1, 1, 42, 28, 4, 12, 12, 60, 90, 18, 2, 56, 8

Offset: 1

Labos Elemer, Apr 26 2001

nonn

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A000203, A058075.

seq(igcd(numtheory:-sigma(n+1),numtheory:-sigma(n)),n=1..100); # Robert Israel, Jul 03 2017

Table[GCD[DivisorSigma[1, n + 1], DivisorSigma[1, n]] , {n, 1, 50}] (* G. C. Greubel, Jul 03 2017 *)

a(n) = { gcd(sigma(n), sigma(n+1)) } \\ Harry J. Smith, Jul 11 2009

a(n) = gcd(A000203(n+1), A000203(n)).

Name corrected by Robert Israel, Jul 03 2017

A058074 Integers m such that gcd(d(m),d(m+1)) = 1, where d(m) is number of positive divisors of m.

Original entry on oeis.org

1, 3, 4, 8, 9, 15, 16, 24, 25, 35, 36, 48, 63, 64, 81, 100, 120, 121, 143, 144, 168, 169, 195, 196, 225, 255, 256, 289, 323, 361, 399, 400, 440, 441, 483, 484, 528, 529, 576, 625, 676, 728, 729, 783, 784, 840, 841, 899, 900, 960, 961, 1023, 1024, 1088, 1089

Offset: 1

Leroy Quet, Nov 11 2000

nonn

If k is a term then either k or k+1 is a square. If k is in A005574 then k^2 is a term. - Amiram Eldar, Aug 08 2020

			8 is included because d(8) = 4 is relatively prime to d(9) = 3.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Jean-Marie De Koninck and Imre Kátai, On the coprimality of some arithmetic functions, Publications de l'Institut Mathématique, 2010 87(101):121-128.

Cf. A005574, A058075.

Select[Range[1100],GCD[DivisorSigma[0,#],DivisorSigma[0,#+1]]==1&] (* Harvey P. Dale, Apr 04 2015 *)

lista(nn) = {for(n=1, nn, if (gcd(numdiv(n), numdiv(n+1)) == 1, print1(n, ", ")));} \\ Michel Marcus, May 19 2014

Offset changed to 1 by Michel Marcus, May 20 2014

Name edited by Michel Marcus, Jan 12 2018

A260963 Numbers n such that gcd(sigma(n), n*(n+1)/2 - sigma(n)) = 1, where sigma(n) is sum of positive divisors of n.

Original entry on oeis.org

1, 4, 9, 10, 16, 21, 22, 25, 34, 36, 46, 49, 57, 58, 64, 70, 81, 82, 85, 93, 94, 100, 106, 118, 121, 129, 130, 133, 142, 144, 154, 166, 169, 178, 201, 202, 205, 214, 217, 225, 226, 237, 238, 250, 253, 256, 262, 265, 274, 289, 298, 301, 309, 310, 322, 324, 325

Offset: 1

Paolo P. Lava, Aug 27 2015

			sigma(10) = 18, 10*11/2 - sigma(10) = 55 - 18 = 37 and gcd(18,37) = 1 because 18 = 2*9 and 37 is prime.

Paolo P. Lava, Table of n, a(n) for n = 1..10000

Cf. A000203, A024816, A055008, A058075.

with(numtheory): P:=proc(q) local n; for n from 1 to q do
if gcd(sigma(n),n*(n+1)/2-sigma(n))=1 then print(n); fi; od; end: P(10^9);

Select[Range@ 360, GCD[DivisorSigma[1, #], # (# + 1)/2 - DivisorSigma[1, #]] == 1 &] (* Michael De Vlieger, Aug 27 2015 *)

cp's OEIS Frontend

A060780 a(n) = gcd(sigma(n+1), sigma(n)), where sigma = A000203.

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A058074 Integers m such that gcd(d(m),d(m+1)) = 1, where d(m) is number of positive divisors of m.

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A260963 Numbers n such that gcd(sigma(n), n*(n+1)/2 - sigma(n)) = 1, where sigma(n) is sum of positive divisors of n.

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Maple

Mathematica