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

1,14

Links

Table of n, a(n) for n=1..94.

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000005 (tau), A005237.

Partial sums of A130638.

Sequence in context: A276798 A067100 A296237 * A071804 A280953 A111894

Adjacent sequences: A074799 A074800 A074801 * A074803 A074804 A074805

Keyword

easy,nonn

Author

Benoit Cloitre, Sep 08 2002

Status

approved