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

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

Author

Leroy Quet, Nov 11 2000

Keywords

• nonn

Comments

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

Examples

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

Links

• 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.

Crossrefs

Cf. A005574, A058075.

Programs

Mathematica

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

PARI

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

Extensions

Offset changed to 1 by Michel Marcus, May 20 2014

Name edited by Michel Marcus, Jan 12 2018