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A019295
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a(n) = sigma(sigma(...(sigma(n))...)) / n, where sigma (A000203) is iterated until a multiple of n is reached.
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7
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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
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1,2
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COMMENTS
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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.
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LINKS
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PROG
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(PARI) apply( {A019295(n, s=n)=while((s=sigma(s))%n, ); s\n}, [1..50]) \\ M. F. Hasler, Jan 08 2020
(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
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CROSSREFS
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Cf. A019276 (megaperfect numbers: where A019294 reaches records), A019276 (record values), A019294 (number of iterations needed to reach a multiple of n).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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