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.

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, 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, 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

Offset: 1

Author

Benoit Cloitre, Sep 08 2002

Keywords

• easy
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005 (tau), A005237.

Partial sums of A130638.

Programs

Mathematica

Accumulate[If[#[[1]]==#[[2]],1,0]&/@Partition[DivisorSigma[ 0,Range[ 100]],2,1]] (* Harvey P. Dale, Jan 27 2021 *)

PARI

a(n)=sum(i=1,n,if(numdiv(i)-numdiv(i+1),0,1))

Formula

Is a(n) asymptotic to c*n with c = 0.1...?

Answer: No, since the asymptotic density of A005237 is 0. See the comments and links at A005237. - Amiram Eldar, Jul 26 2025