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Revision History for A245782

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Showing entries 1-10 | older changes

A245782

Refactorable multiply-perfect numbers.
(history; published version)

#19 by OEIS Server at Thu May 09 02:53:08 EDT 2024

LINKS

Amiram Eldar, <a href="/A245782/b245782_1.txt">Table of n, a(n) for n = 1..407</a>

#18 by Michel Marcus at Thu May 09 02:53:08 EDT 2024

STATUS

reviewed

approved

Discussion

Thu May 09

02:53

OEIS Server: Installed first b-file as b245782.txt.

#17 by Joerg Arndt at Thu May 09 02:48:24 EDT 2024

STATUS

proposed

reviewed

#16 by Amiram Eldar at Thu May 09 02:45:06 EDT 2024

STATUS

editing

proposed

#15 by Amiram Eldar at Thu May 09 02:06:27 EDT 2024

CROSSREFS

Intersection of A033950 (refactorable numbers) and A007691 (multiply-perfect numbers).

#14 by Amiram Eldar at Thu May 09 02:05:59 EDT 2024

COMMENTS

Subsequence of A245778 and A245786.

Supersequence of A047728.

Intersection of A033950 (refactorable numbers) and A007691 (multiply-perfect numbers).

CROSSREFS

Subsequence of A245778 and A245786.

Supersequence of A047728.

Intersection of A033950 (refactorable numbers) and A007691 (multiply-perfect numbers).

Cf. A000005, A000203, A007691, A047728.

Cf. A245776, A245777, A245778, A245779, A245786.

#13 by Amiram Eldar at Thu May 09 01:22:13 EDT 2024

COMMENTS

Multiply-perfect numbers n k (A007691) such that n k / tau(nk) is integer.

Also multiply-perfect numbers n k (A007691) such that (n k / tau(nk) - sigma(nk) / nk) = (n k / A000005(nk) - A000203(nk) / nk) is integer.

Also multiply-perfect numbers n k (A007691) such that (n k / tau(nk) + sigma(nk) / nk) = (n k / A000005(nk) + A000203(nk) / nk) is integer.

#12 by Amiram Eldar at Thu May 09 01:20:21 EDT 2024

MATHEMATICA

q[n_] := Module[{d = DivisorSigma[0, n], s = DivisorSigma[1, n]}, Divisible[s, n] && Divisible[n, d]]; Select[Range[31000], q] (* Amiram Eldar, May 09 2024 *)

PROG

(PARI) is(k) = {my(f = factor(k), s = sigma(f), d = numdiv(f)); !(s % k) && !(k % d); } \\ Amiram Eldar, May 09 2024

#11 by Amiram Eldar at Thu May 09 01:19:40 EDT 2024

LINKS

Amiram Eldar, <a href="/A245782/b245782_1.txt">Table of n, a(n) for n = 1..407</a>

#10 by Amiram Eldar at Thu May 09 01:19:20 EDT 2024

DATA

1, 672, 30240, 23569920, 45532800, 14182439040, 153003540480, 403031236608, 518666803200, 13661860101120, 740344994887680, 796928461056000, 212517062615531520, 87934476737668055040, 154345556085770649600, 170206605192656148480, 1161492388333469337600, 1802582780370364661760

KEYWORD

nonn,more

nonn

EXTENSIONS

a(14)-a(18) from Amiram Eldar, May 09 2024

STATUS

approved

editing