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

1,2

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

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.

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A005574, A058075.

Sequence in context: A186775 A285440 A135276 * A319875 A123722 A328733

Adjacent sequences: A058071 A058072 A058073 * A058075 A058076 A058077

Keyword

nonn

Author

Leroy Quet, Nov 11 2000

Extensions

Offset changed to 1 by Michel Marcus, May 20 2014

Name edited by Michel Marcus, Jan 12 2018

Status

approved