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A176802 a(n) = the smallest natural numbers m such that product of harmonic mean of the divisors of n and harmonic mean of the divisors of m are integers. 0
1, 3, 2, 7, 27, 1, 4, 3, 182, 27, 270, 14, 126, 4, 6, 31, 1638, 91, 980, 6, 32, 84, 4455, 15, 248, 63, 10, 1, 8190, 3, 16, 21, 672, 819, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Harmonic mean of the divisors of number n is rational number b(n) = n*A000005(n) / A000203(n) = A099377(n) / A099378(n). a(n) = 1 for infinitely many n. a(n) = 1 for numbers from A001599: a(A001599(n)) = 1. a(n) = 1 iff A099378(n) = 1.

LINKS

Table of n, a(n) for n=1..35.

EXAMPLE

For n = 4; b(4) = 12/7, a(n) = 7 because b(7) = 7/4; 12/7 * 7/4 = 3 (integer).

CROSSREFS

Sequence in context: A248054 A329421 A100985 * A230710 A265009 A021757

Adjacent sequences:  A176799 A176800 A176801 * A176803 A176804 A176805

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Apr 26 2010

STATUS

approved

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Last modified January 27 12:01 EST 2020. Contains 331295 sequences. (Running on oeis4.)