[go: up one dir, main page]

login
Revision History for A008480 (Bold, blue-underlined text is an addition; faded, red-underlined text is a deletion.)

Showing entries 1-10 | older changes
Number of ordered prime factorizations of n.
(history; published version)
#122 by Michel Marcus at Fri Mar 08 08:05:57 EST 2024
STATUS

reviewed

approved

#121 by Joerg Arndt at Fri Mar 08 07:55:45 EST 2024
STATUS

proposed

reviewed

#120 by Amiram Eldar at Fri Mar 08 03:42:19 EST 2024
STATUS

editing

proposed

#119 by Amiram Eldar at Fri Mar 08 03:23:20 EST 2024
LINKS

Maxie D. Schmidt, <a href="https://arxiv.org/abs/2102.05842">New characterizations Exact formulas for partial sums of the summatory Möbius function of expressed by partial sums weighted by the Moebius Liouville lambda function</a>, arXiv:2102.05842 [math.NT], 2021-2022.

#118 by Amiram Eldar at Fri Mar 08 03:21:52 EST 2024
REFERENCES

A. Knopfmacher, J. Knopfmacher , and R. Warlimont, "Ordered factorizations for integers and arithmetical semigroups", in Advances in Number Theory, (Proc. 3rd Conf. Canadian Number Theory Assoc., 1991), Clarendon Press, Oxford, 1993, pp. 151-165.

#117 by Amiram Eldar at Fri Mar 08 03:20:39 EST 2024
REFERENCES

S. Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 292-295.

LINKS

S. Steven R. Finch, <a href="/A001055/a001055.pdf">Kalmar's composition constant</a>, June 5, 2003. [Cached copy, with permission of the author]

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MultinomialCoefficient.html">Multinomial Coefficient</a>.

#116 by Amiram Eldar at Fri Mar 08 03:19:33 EST 2024
FORMULA

a(n) = A130675(n)/A112624(n). - Amiram Eldar, Mar 08 2024

CROSSREFS
KEYWORD

nonn,easy

STATUS

approved

editing

#115 by N. J. A. Sloane at Sat Aug 05 21:21:00 EDT 2023
STATUS

proposed

approved

#114 by Chai Wah Wu at Sat Aug 05 16:11:20 EDT 2023
STATUS

editing

proposed

#113 by Chai Wah Wu at Sat Aug 05 16:10:54 EDT 2023
PROG

(Python)

from math import prod, factorial

from sympy import factorint

def A008480(n): return factorial(sum(f:=factorint(n).values()))//prod(map(factorial, f)) # Chai Wah Wu, Aug 05 2023

STATUS

approved

editing