A392925 - OEIS

%I #52 Jun 03 2026 16:08:55

%S 65,3913,5617,1717,65,145,6069,135,65,3417,5617,1431,65,231,2350089,

%T 10131,65,98045,5617,145,65,134667,32079,1717,65,135,5617,22633,65,

%U 6341,2350089,483,65,145,5617,224321,65,1113,4097,475839,65,7745,5617,135,65,10345

%N Smallest odd number k greater than 1 such that sigma_n(k)/k is an integer.

%C a(1) corresponds to odd multiperfect numbers greater than 1, if they exist.

%C Does every integer greater than 1 have a solution?

%C 65 is a solution for every positive n congruent to 2 mod 4.

%H Alexander Violette, <a href="/A392925/b392925.txt">Table of n, a(n) for n = 2..200</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Divisor_function">Divisor function</a>

%e 65 is the smallest odd number k > 1 such that sigma_2(k)/k is an integer, hence a(2)=65.

%o (PARI) a(n) = my(k=3); while (sigma(k,n) % k, k+=2); k; \\ _Michel Marcus_, May 30 2026

%Y Cf. A000203, A066135 (even), A007691 (mpn).

%K nonn

%O 2,1

%A _Alexander Violette_, May 13 2026