A019295 - OEIS

%I #35 Nov 19 2025 09:59:16

%S 1,2,5,2,24,2,24,3,168,12,1834560,10,84480,12,4,2,92520,20,62720,84,3,

%T 49920,6516224,7,881280,28,3360,2,

%U 517517500266693633076805172570524811961093324800,728,912,18,19767296,46260,144,42,30349648609280,38644089120,30,663,34042889727216750428160

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

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

%C See also the Cohen-te Riele links in A019276.

%H Graeme L. Cohen and Herman J. J. te Riele, <a href="http://projecteuclid.org/euclid.em/1047565640">Iterating the sum-of-divisors function</a>, Experimental Mathematics, 5(2) (1996), pp. 91-100.

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

%o (Magma) f:=func<n|DivisorSigma(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

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

%K nonn

%O 1,2

%A _N. J. A. Sloane_

%E More terms from _Max Alekseyev_, Sep 22 2016

%E Edited by _M. F. Hasler_, Jan 08 2020