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A283495
Smallest k such that there is a number whose divisors sum to k*n.
0
1, 2, 1, 1, 3, 1, 1, 1, 2, 2, 4, 1, 1, 2, 1, 2, 4, 1, 2, 1, 2, 2, 6, 1, 6, 3, 2, 1, 6, 2, 1, 1, 4, 2, 4, 1, 2, 1, 1, 1, 4, 1, 6, 1, 2, 3, 6, 1, 2, 3, 2, 2, 4, 1, 2, 1, 1, 3, 6, 1, 3, 2, 1, 2, 3, 2, 6, 1, 2, 2, 4, 1, 7, 1, 2, 2, 4, 1, 2, 1, 2, 2, 4, 1, 3, 3, 2, 2, 23, 1, 1, 4, 1, 3, 6, 1
OFFSET
1,2
COMMENTS
Smallest k >=1 such that (number of numbers whose divisor sum to k*n) = m:
m \n| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
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0 | 2 | 1 | 3 | 4 | 1 | 11 | 3 | 2 | 1 | 1 | 1 | 23 |
1 | 1 | 2 | 1 | 1 | 3 | 1 | 1 | 1 | 2 | 2 | 4 | 3 |
2 | 12 | 6 | 4 | 3 | 16 | 2 | 8 | 4 | 2 | 8 | 12 | 1 |
3 | 24 | 12 | 8 | 6 | 12 | 4 | 6 | 3 | 10 | 6 | ...| |
...
EXAMPLE
a(2) = 2 because (number of numbers whose divisor sum to 2*2) = 1.
PROG
(PARI) a(n)=my(k=oo, m, t); while(m<k, t=sigma(m++)/n; if(denominator(t)==1 && t<k, k=t)); k \\ Charles R Greathouse IV, Mar 09 2017
CROSSREFS
Cf. A007369 (numbers n such that a(n) > 1).
Sequence in context: A135010 A138138 A230440 * A196931 A175465 A080209
KEYWORD
nonn
AUTHOR
EXTENSIONS
Corrected by Charles R Greathouse IV, Mar 09 2017
STATUS
approved