A097015 Smallest k such that sigma(k) + 1 is divisible by primorial(n).

1, 1, 2401, 2614689, 36324729, 36324729, 2411675443849, 2411675443849, 12361036649679601

Offset

0,3

Comments

10^19 < a(9) <= 725298909352131113041. Terms a(3) through a(8) all have the prime signature p^4*q^2*r^2. Any x such that sigma(x) = -1 (mod 30) must have at least eight prime factors. However, for all n, there are solutions with fewer than three distinct prime factors. More generally, for any k > 1, let p be a prime of the form mk+1; then sigma(p^(k-2)) = -1 (mod k). For a(9), 725298909352131113041 is the least solution with eight prime factors. I have not been able to rule out a smaller solution with more prime factors. - David Wasserman, Dec 14 2007

Links

Table of n, a(n) for n=0..8.

Formula

a(n) = A233929(A002110(n)). - Andrew Howroyd, Dec 12 2024

Crossrefs

Cf. A002110 (primorial), A084301, A084303, A000203, A097011, A097012, A097014, A233929.

Sequence in context: A017608 A061210 A226092 * A222461 A013845 A352730

Adjacent sequences: A097012 A097013 A097014 * A097016 A097017 A097018

Keyword

nonn

Author

Labos Elemer, Aug 19 2004

Extensions

More terms from David Wasserman, Dec 14 2007

a(0)=1 prepended by Andrew Howroyd, Dec 12 2024

Status

approved