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.
%I A074802 #21 Jul 26 2025 14:38:56 %S A074802 0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,4,5,6, %T A074802 6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9, %U A074802 9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,11,12,12,12,12,12,12,12,13,14 %N A074802 Number of numbers k <= n such that tau(k) = tau(k+1) where tau(x) = A000005(x) is the number of divisors of x. %H A074802 Amiram Eldar, <a href="/A074802/b074802.txt">Table of n, a(n) for n = 1..10000</a> %F A074802 Is a(n) asymptotic to c*n with c = 0.1...? %F A074802 Answer: No, since the asymptotic density of A005237 is 0. See the comments and links at A005237. - _Amiram Eldar_, Jul 26 2025 %t A074802 Accumulate[If[#[[1]]==#[[2]],1,0]&/@Partition[DivisorSigma[ 0,Range[ 100]],2,1]] (* _Harvey P. Dale_, Jan 27 2021 *) %o A074802 (PARI) a(n)=sum(i=1,n,if(numdiv(i)-numdiv(i+1),0,1)) %Y A074802 Cf. A000005 (tau), A005237. %Y A074802 Partial sums of A130638. %K A074802 easy,nonn %O A074802 1,14 %A A074802 _Benoit Cloitre_, Sep 08 2002