A176801 a(n) is the smallest natural number m such that product of arithmetic mean of the divisors of n and arithmetic mean of the divisors of m is an integer.

1, 3, 1, 5, 1, 1, 1, 7, 5, 3, 1, 2, 1, 1, 1, 19, 1, 3, 1, 1, 1, 1, 1, 3, 5, 3, 1, 2, 1, 1, 1, 3, 1, 3, 1, 17, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 19, 1, 3, 1, 5, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 13, 1, 1, 1, 1, 1, 1, 1, 7, 1, 3, 2, 2, 1, 1, 1, 19, 19, 3, 1, 2, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 17, 1, 1, 1, 7, 1

Offset: 1

Author

Jaroslav Krizek, Apr 26 2010

Keywords

• nonn

Comments

a(n) = 1 for infinitely many n.

a(n) = 1 for numbers from A003601: a(A003601(n)) = 1.

a(n) = 1 iff A057021(n) = 1.

Not all terms are 1's or primes. For example, a(128) = 21. - Antti Karttunen, Dec 24 2018

Examples

			For n = 12; b(12) = 14/3, a(n) = 2 because b(2) = 3/2; 14/3 * 3/2 = 7 (integer).
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A000005/A000203 or A057020/A057021: arithmetic mean.

Cf. A003601, A245656.

Programs

PARI

A176801(n) = { my(am=(sigma(n)/numdiv(n))); for(i=1, oo, if(1==denominator(am*(sigma(i)/numdiv(i))), return(i))); }; \\ Antti Karttunen, Dec 24 2018

Extensions

More terms from Antti Karttunen, Dec 24 2018