A089363 Numbers of pairs (i, j), i, j > 1, such that i^j <= 10^n.

3, 16, 50, 145, 407, 1177, 3508, 10677, 32967, 102719, 321798, 1011538, 3186390, 10050746, 31730137, 100228044, 316713624, 1001037551, 3164497350, 10004755379, 31632975601, 100021893197, 316274794667, 1000101078155

Offset

1,1

Comments

These numbers are related to the divergent series r sum(n^(1/k) = n^1/2 + n^1/3 + ...n^1/r for abs(n) > 0 and r=sqrt(n). k=2

Links

Table of n, a(n) for n=1..24.

Formula

a(n) = A089361(10^n) = sum_{p = 2..inf} [floor(10^(n/p)) - 1]. - David Wasserman, Sep 14 2005

Example

There are 16 perfect powers <= 100: 2^2, 2^3, 3^2, 2^4, 4^2, 5^2, 3^3, 2^5, 6^2, 7^2, 2^6, 4^3, 8^2, 3^4, 9^2, 10^2

Prog

(PARI) plessn10(n, m) = { for(k=1, n, s=0; z = 10^k; r = floor(sqrt(z)); for(x=m, r, for(y=2, r, p = floor(x^y); if(p<=z, s++) ) ); print1(s", ") ) }

Crossrefs

Sequence in context: A222843 A346556 A004320 * A000574 A041233 A055194

Adjacent sequences: A089360 A089361 A089362 * A089364 A089365 A089366

Keyword

nonn

Author

Cino Hilliard, Dec 27 2003

Extensions

More terms from David Wasserman, Sep 14 2005

Status

approved