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A283486
Number of k such that sigma(k) = 2n where sigma(m) = A000203(m) is the sum of the divisors of m.
2
0, 1, 1, 1, 0, 2, 1, 0, 2, 1, 0, 3, 0, 1, 1, 2, 0, 1, 1, 1, 3, 1, 0, 3, 0, 0, 2, 2, 0, 3, 1, 0, 0, 1, 0, 5, 1, 0, 1, 2, 0, 3, 0, 0, 3, 0, 0, 4, 2, 0, 1, 2, 0, 2, 1, 1, 2, 0, 0, 4, 0, 2, 2, 2, 0, 2, 0, 0, 1, 2, 0, 5, 0, 0, 1, 2, 0, 2, 1, 1, 1, 1, 0, 6, 0, 0, 1, 1, 0, 4, 2, 0, 2, 0, 0, 5
OFFSET
1,6
COMMENTS
First occurrence of k: 1, 2, 6, 12, 48, 36, 84, ...
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = A054973(2n) - Michel Marcus, Mar 08 2017.
EXAMPLE
a(12) = 3 because sigma(14) = 1 + 2 + 7 + 14 = 24, sigma(15) = 1 + 3 + 5 + 15 = 24 and sigma(23) = 1 + 23 = 24.
PROG
(PARI) first(n)=my(v=vector(n), t); for(k=1, 2*n-1, t=sigma(k)/2; if(t<=n && denominator(t)==1, v[t]++)); v \\ Charles R Greathouse IV, Mar 08 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(96) corrected by Charles R Greathouse IV, Mar 08 2017
STATUS
approved