A019295 a(n) = sigma(sigma(...(sigma(n))...)) / n, where sigma (A000203) is iterated until a multiple of n is reached.

1, 2, 5, 2, 24, 2, 24, 3, 168, 12, 1834560, 10, 84480, 12, 4, 2, 92520, 20, 62720, 84, 3, 49920, 6516224, 7, 881280, 28, 3360, 2, 517517500266693633076805172570524811961093324800, 728, 912, 18, 19767296, 46260, 144, 42, 30349648609280, 38644089120, 30, 663, 34042889727216750428160

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

The minimal number of iterations of the sigma function until a multiple of n is reached (after the initial n) is given in A019294.

See also the Cohen-te Riele links in A019276.

Links

• Graeme L. Cohen and Herman J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100.
• Experimental Mathematics, Volume 5 (1996) ["Outdated Archival Version" as of 2005.]

Crossrefs

Cf. A019276 (megaperfect numbers: where A019294 reaches records), A019276 (record values), A019294 (number of iterations needed to reach a multiple of n).

Programs

Magma

f:=func; a:=[]; for n in [1..41] do k:=n; while f(k) mod n ne 0 do k:=f(k); end while; Append(~a,f(k) div n); end for; a; // Marius A. Burtea, Jan 11 2020

PARI

apply( {A019295(n,s=n)=while((s=sigma(s))%n,);s\n}, [1..50]) \\ M. F. Hasler, Jan 08 2020

Extensions

More terms from Max Alekseyev, Sep 22 2016

Edited by M. F. Hasler, Jan 08 2020