

A019295


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


7



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
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OFFSET

1,2


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 Cohente Riele links in A019276.


LINKS

Table of n, a(n) for n=1..41.
Graeme L. Cohen and Herman J. J. te Riele, Iterating the sumofdivisors function, Experimental Mathematics, 5 (1996), pp. 93100.
Experimental Mathematics, Volume 5 (1996) ["Outdated Archival Version" as of 2005.]


PROG

(PARI) apply( {A019295(n, s=n)=while((s=sigma(s))%n, ); s\n}, [1..50]) \\ M. F. Hasler, Jan 08 2020
(MAGMA) f:=func<nDivisorSigma(1, n)>; 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


CROSSREFS

Cf. A019276 (megaperfect numbers: where A019294 reaches records), A019276 (record values), A019294 (number of iterations needed to reach a multiple of n).
Sequence in context: A286452 A298664 A319201 * A328264 A170908 A229029
Adjacent sequences: A019292 A019293 A019294 * A019296 A019297 A019298


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Max Alekseyev, Sep 22 2016
Edited by M. F. Hasler, Jan 08 2020


STATUS

approved



