The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A347048 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A347048

Number of even-length ordered factorizations of n with integer alternating product.
(history; published version)

#18 by OEIS Server at Sun Jul 28 10:05:23 EDT 2024

LINKS

Antti Karttunen, <a href="/A347048/b347048_1.txt">Table of n, a(n) for n = 1..65537</a>

#17 by Michael De Vlieger at Sun Jul 28 10:05:23 EDT 2024

STATUS

proposed

approved

Discussion

Sun Jul 28

10:05

OEIS Server: Installed first b-file as b347048.txt.

#16 by Antti Karttunen at Sun Jul 28 09:38:04 EDT 2024

STATUS

editing

proposed

#15 by Antti Karttunen at Sun Jul 28 05:13:20 EDT 2024

PROG

(PARI) A347048(n, m=n, ap=1, e=0) = if(1==n, !(e%2) && 1==denominatornumerator(ap), sumdiv(n, d, if(d>1, A347048(n/d, d, ap * d^((-1)^e), 1-e)))); \\ Antti Karttunen, Jul 28 2024

Discussion

Sun Jul 28

05:24

Antti Karttunen: Program
A347048(n, m=n, ap=1, e=0) = if(1==n,!(e%2) && 1==denominator(ap), sumdiv(n, d, if(d>1, A347048(n/d, d, ap * d^((-1)^e), 1-e))));
works also, because it just counts the same factorizations, but reversed.

#14 by Antti Karttunen at Sun Jul 28 05:07:31 EDT 2024

LINKS

<a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

#13 by Antti Karttunen at Sun Jul 28 05:04:57 EDT 2024

LINKS

Antti Karttunen, <a href="/A347048/b347048_1.txt">Table of n, a(n) for n = 1..65537</a>

#12 by Antti Karttunen at Sun Jul 28 05:00:01 EDT 2024

DATA

1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 3, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 4, 0, 0, 0, 7, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 6, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 11, 0, 0, 0, 1, 0, 0, 0, 11, 0, 0, 1, 1, 0, 0, 0, 6, 3, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 8, 0, 1, 1, 7, 0, 0, 0, 1, 0

PROG

(PARI) A347048(n, m=n, ap=1, e=0) = if(1==n, !(e%2) && 1==denominator(ap), sumdiv(n, d, if(d>1, A347048(n/d, d, ap * d^((-1)^e), 1-e)))); \\ Antti Karttunen, Jul 28 2024

EXTENSIONS

Data section extended up to a(105) by Antti Karttunen, Jul 28 2024

STATUS

approved

editing

#11 by Susanna Cuyler at Wed Oct 27 22:22:12 EDT 2021

STATUS

proposed

approved

#10 by Gus Wiseman at Sun Oct 17 02:12:53 EDT 2021

STATUS

editing

proposed

#9 by Gus Wiseman at Fri Oct 15 15:07:39 EDT 2021

CROSSREFS

A347050 counts = factorizations with an alternating permutation, complement A347706.

A347706 counts factorizations with no alternating permutations.