The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A293448 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A293448

Self-inverse permutation of natural numbers: replace (with multiplicity) each prime factor A000040(k) with A000040(min+(max-k)) in the prime factorization of n, where min = A055396(n) and max = A061395(n).
(history; published version)

#26 by Bruno Berselli at Fri Nov 24 04:32:59 EST 2017

STATUS

reviewed

approved

#25 by Michael B. Porter at Fri Nov 24 04:21:31 EST 2017

STATUS

proposed

reviewed

#24 by Rémy Sigrist at Fri Nov 24 00:23:42 EST 2017

STATUS

editing

proposed

#23 by Rémy Sigrist at Fri Nov 24 00:23:34 EST 2017

COMMENTS

a(n) = n iff n belongs to A236510. _- _Rémy Sigrist_, Nov 22 2017

STATUS

proposed

editing

#22 by Rémy Sigrist at Wed Nov 22 14:35:07 EST 2017

STATUS

editing

proposed

#21 by Rémy Sigrist at Wed Nov 22 14:29:39 EST 2017

COMMENTS

a(n) = n iff n belongs to A236510. Rémy Sigrist, Nov 22 2017

CROSSREFS

Cf. A000720, A055396, A057889, A061395, A236510 (fixed points), A273258.

STATUS

approved

editing

Discussion

Wed Nov 22

14:35

Rémy Sigrist: added fixed points

#20 by Susanna Cuyler at Tue Nov 21 21:35:49 EST 2017

STATUS

proposed

approved

#19 by Antti Karttunen at Tue Nov 21 09:45:32 EST 2017

STATUS

editing

proposed

#18 by Antti Karttunen at Tue Nov 21 09:44:22 EST 2017

EXAMPLE

For n = 126 = 2 * 3^2 * 7 = prime(1) * prime(2)^2 * prime(4), thus min = 1 and max = 4, so we form a product prime(1+(4-1)) * prime(1+(4-2))^2 * prime(1+(4-4)), thus a(126) = prime(4) * prime(3)^2 * prime(1) = 7 * 5^2 * 2 = 350.

#17 by Antti Karttunen at Tue Nov 21 09:42:26 EST 2017

COMMENTS

Reverse the prime-indices in such a way that A055396(n) the smallest and A061395(the greatest prime dividing n (A020639 and A006530) are preserved.