A246909 a(n) = the smallest numbers k such that sigma(k+sigma(k)) = n*sigma(k) or -1 if no solution exists or has been found for n.

-1, 2, 1, 28, 15456, 831376

Offset

1,2

Comments

a(7) > 10^7 or -1.

a(7) > 10^10 or -1. - Jason Yuen, Dec 21 2025

Links

Table of n, a(n) for n=1..6.

Example

Sequence of numbers k such that sigma(k+sigma(k)) = n*sigma(k) for 1 <= n <= 6:
n = 2: 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, ... (A246857).
n = 3: 1, 7, 26, 30, 42, 54, 69, 78, 84, 94, 102, 103, 114, ... (A246910).
n = 4: 28, 66, 348, 496, 840, 920, 1320, 1416, 1602, 1770, ... (A246911).
n = 5: 15456, 16920, 48576, 59520, 107160, 153360, 232596, ... (A246912).
n = 6: 831376, 3944688, 16956576, 17843616, ... (A246913).

Prog

(Magma) A246909:=func<n|exists(r){m: m in[1..1000000] | SumOfDivisors(m+SumOfDivisors(m))eq n*SumOfDivisors(m)}select r else-1>; [A246909(n): n in[1..10]];

Crossrefs

Cf. A000203, A246910, A246911, A246912, A246913, A246914.

Sequence in context: A012660 A015155 A009822 * A249269 A245621 A349037

Adjacent sequences: A246906 A246907 A246908 * A246910 A246911 A246912

Keyword

sign,hard,more

Author

Jaroslav Krizek, Sep 07 2014

Status

approved