cp's OEIS Frontend

A239578 Smallest number m such that the numerator of sigma(m)/m is equal to n, or zero if no such m exists.

%I A239578 #18 Feb 22 2020 20:54:24
%S A239578 1,6,2,3,24,5,4,7,10,1080,35640,11,9,13,8,33,297600,17,588,19,20,1782,
%T A239578 1907020800,23,216,45,34,78
%N A239578 Smallest number m such that the numerator of sigma(m)/m is equal to n, or zero if no such m exists.
%C A239578 If n-1 is prime, a(n) = n-1.
%C A239578 a(29) <= 1176249221876579007725568000.
%C A239578 Index of first occurrence of n in A017665. - _Michel Marcus_, Mar 24 2014
%H A239578 Giovanni Resta, <a href="/A239578/a239578.txt">Terms a(n) < 10^12, for n <= 1000</a>
%e A239578 a(2) = 6 since 6 is the first perfect number, with 2 as the numerator of sigma(6)/6.
%e A239578 a(3) = 2 because sigma(2)/2 = 3/2 and it is the first number that gives this numerator.
%o A239578 (PARI) a(n) = {k = 1; while (numerator(sigma(k)/k) != n, k++); k;}
%Y A239578 Cf. A017665 (numerator of sigma(n)/n), A162657 (similar sequence but related to denominators).
%K A239578 nonn,more
%O A239578 1,2
%A A239578 _Michel Marcus_, Mar 21 2014
%E A239578 a(23) = 1907020800 confirmed by _Giovanni Resta_, Mar 21 2014