cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A058074 #29 Aug 08 2020 08:23:11
%S A058074 1,3,4,8,9,15,16,24,25,35,36,48,63,64,81,100,120,121,143,144,168,169,
%T A058074 195,196,225,255,256,289,323,361,399,400,440,441,483,484,528,529,576,
%U A058074 625,676,728,729,783,784,840,841,899,900,960,961,1023,1024,1088,1089
%N A058074 Integers m such that gcd(d(m),d(m+1)) = 1, where d(m) is number of positive divisors of m.
%C A058074 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
%H A058074 Amiram Eldar, <a href="/A058074/b058074.txt">Table of n, a(n) for n = 1..10000</a>
%H A058074 Jean-Marie De Koninck and Imre Kátai, <a href="https://www.emis.de/journals/PIMB/101/9.html">On the coprimality of some arithmetic functions</a>, Publications de l'Institut Mathématique, 2010 87(101):121-128.
%e A058074 8 is included because d(8) = 4 is relatively prime to d(9) = 3.
%t A058074 Select[Range[1100],GCD[DivisorSigma[0,#],DivisorSigma[0,#+1]]==1&] (* _Harvey P. Dale_, Apr 04 2015 *)
%o A058074 (PARI) lista(nn) = {for(n=1, nn, if (gcd(numdiv(n), numdiv(n+1)) == 1, print1(n, ", ")));} \\ _Michel Marcus_, May 19 2014
%Y A058074 Cf. A005574, A058075.
%K A058074 nonn
%O A058074 1,2
%A A058074 _Leroy Quet_, Nov 11 2000
%E A058074 Offset changed to 1 by _Michel Marcus_, May 20 2014
%E A058074 Name edited by _Michel Marcus_, Jan 12 2018