A337176 Number of pairs of divisors of n, (d1,d2), such that d1 <= d2 and d1*d2 < sqrt(n).

0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 4, 1, 4, 2, 3, 1, 5, 1, 3, 2, 4, 1, 5, 1, 4, 2, 3, 2, 5, 1, 3, 2, 5, 1, 6, 1, 4, 3, 3, 1, 7, 1, 4, 2, 4, 1, 6, 2, 5, 2, 3, 1, 8, 1, 3, 3, 4, 2, 6, 1, 5, 2, 5, 1, 9, 1, 3, 3, 5, 2, 6, 1, 7, 2, 3, 1, 10, 2, 3, 3, 6, 1, 9, 2, 5

Offset

1,6

Comments

a(n) = 1 iff n is prime or n is the square of a prime (A000430). - Bernard Schott, Jan 30 2021

Links

Table of n, a(n) for n=1..92.

Formula

a(n) = Sum_{d1|n, d2|n} (1 - sign(floor(d1*d2/sqrt(n)))).

Example

a(24) = 5; (1,1), (1,2), (1,3), (1,4), (2,2).
a(25) = 1; (1,1).
a(26) = 3; (1,1), (1,2), (2,2).
a(27) = 2; (1,1), (1,3).

Mathematica

Table[Sum[Sum[(1 - Sign[Floor[(i*k)/Sqrt[n]]]) (1 - Ceiling[n/k] + Floor[n/k]) (1 - Ceiling[n/i] + Floor[n/i]), {i, k}], {k, n}], {n, 80}]

Crossrefs

Cf. A337175.

Sequence in context: A320889 A296133 A338649 * A033103 A245661 A302789

Adjacent sequences: A337173 A337174 A337175 * A337177 A337178 A337179

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 28 2021

Status

approved