A176803 a(n) = the smallest natural numbers m such that product of antiharmonic mean of the divisors of n and antiharmonic mean of the divisors of m are integers, a(n) = 0 if no such number exists.

1, 4, 0, 1, 4, 0, 0, 4, 1, 100, 0, 0, 9, 0, 0, 1, 100, 4, 0, 1, 0, 0, 0, 0, 1, 25, 0, 0, 325, 0

Offset

1,2

Comments

Antiharmonic mean of the divisors of number n is rational number b(n) = A001157(n) / A000203(n) = A158274(n) / A158275(n). a(n) = 1 for infinitely many n. a(n) = 1 for numbers from A020487: a(A020487(n)) = 1. a(n) = 1 iff A158275(n) = 1. a(n) = 0 for infinitely many n. a(n) = 0 for even A158275(n).

Links

Table of n, a(n) for n=1..30.

Example

For n = 10; b(10) = 65/9, a(n) = 100 because b(100) = 63; 65/9 * 63 = 455 (integer).

Crossrefs

Sequence in context: A096008 A122873 A221275 * A115636 A115715 A292143

Adjacent sequences: A176800 A176801 A176802 * A176804 A176805 A176806

Keyword

nonn

Author

Jaroslav Krizek, Apr 26 2010

Status

approved