The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A368413

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A368413

Number of factorizations of n into positive integers > 1 such that it is not possible to choose a different prime factor of each factor.
(history; published version)

#21 by Michael De Vlieger at Wed Mar 06 14:47:25 EST 2024

STATUS

proposed

approved

#20 by Gus Wiseman at Wed Mar 06 14:25:06 EST 2024

STATUS

editing

proposed

#19 by Gus Wiseman at Wed Mar 06 14:24:58 EST 2024

COMMENTS

The complement is counted by A368414.

CROSSREFS

The complement is counted by A368414.

Cf. A340596, A340653, A367769, A367901, A368187, A368412, A368414.

STATUS

proposed

editing

#18 by Gus Wiseman at Wed Mar 06 14:14:16 EST 2024

STATUS

editing

proposed

#17 by Gus Wiseman at Wed Mar 06 14:13:55 EST 2024

CROSSREFS

For divisors instead of prime factors: A370813, complement A370814.

#16 by Gus Wiseman at Fri Mar 01 05:54:02 EST 2024

COMMENTS

For example, the factorization f = 2*3*6 has three two ways to choose a different prime factor of each factor, namely (2,3,2), (2,3,3), and (2,3,63), and the last but neither of these has all different elements, so f is not counted under a(36).

STATUS

approved

editing

#15 by Amiram Eldar at Thu Feb 15 02:38:19 EST 2024

STATUS

reviewed

approved

#14 by Joerg Arndt at Thu Feb 15 01:49:42 EST 2024

STATUS

proposed

reviewed

#13 by Michel Marcus at Thu Feb 15 01:41:29 EST 2024

STATUS

editing

proposed

#12 by Michel Marcus at Thu Feb 15 01:41:24 EST 2024

FORMULA

A368413a(n) + A368414(n) = A001055(n).

STATUS

approved

editing