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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.
5
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
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
Sequence in context: A186775 A285440 A135276 * A319875 A123722 A328733
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