



1, 2, 1, 4, 9, 7, 25, 8, 13, 7, 17, 10, 121, 27, 169, 16, 29, 39, 289, 12, 37, 19, 41, 26, 529, 47, 19, 133, 53, 34, 841, 32, 61, 31, 43, 93, 29, 35, 73, 217, 81, 63, 23, 50, 21, 43, 89, 58, 2209, 75, 97, 77, 101, 40, 2809, 36, 109, 343, 113, 74, 3481, 65, 3721
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OFFSET

0,2


COMMENTS

a(n) is the denominator of sigma(m)/m when m is A243512(n), the least integer i such that sigma(i)/i = (k+n)/k for some k.


LINKS

Michel Marcus, Table of n, a(n) for n = 0..629


FORMULA

a(n) = A017665(A243512(n))  n.


EXAMPLE

For n=2, A243512(2) is 120 with sigma(120)/120=3/1 and 3/1=(2+1)/1 so a(2)=1.
For n=3, A243512(3) is 4 with sigma(4)/4=7/4 and 7/4=(4+3)/4 so a(3)=4.


MATHEMATICA

f[n_] := Block[{r = DivisorSigma[1, n]/n}, Numerator[r]  Denominator@ r]; Denominator[DivisorSigma[1, #]] & /@ Table[i = 1; While[f@ i != n, i++]; i, {n, 0, 62}] (* Michael De Vlieger, Sep 10 2015 *)


PROG

(PARI) oksk(n, k) = {my(ab = sigma(k, 1)); numerator(ab) == denominator(ab)+n; }
a(n) = {my(k=1); while(!oksk(n, k), k++); denominator(sigma(k, 1)); }


CROSSREFS

Cf. A017665, A017666, A243473, A243512.
Sequence in context: A325016 A077160 A228043 * A057046 A163547 A015943
Adjacent sequences: A262063 A262064 A262065 * A262067 A262068 A262069


KEYWORD

nonn


AUTHOR

Michel Marcus, Sep 10 2015


STATUS

approved



