The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A073576 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A073576

Number of partitions of n into squarefree parts.
(history; published version)

#49 by Michael De Vlieger at Fri Aug 23 10:03:12 EDT 2024

STATUS

reviewed

approved

#48 by Michel Marcus at Fri Aug 23 10:01:34 EDT 2024

STATUS

proposed

reviewed

#47 by Chai Wah Wu at Fri Aug 23 09:55:19 EDT 2024

STATUS

editing

proposed

#46 by Chai Wah Wu at Fri Aug 23 09:54:29 EDT 2024

PROG

(Python)

from functools import lru_cache

from sympy import mobius, divisors

@lru_cache(maxsize=None)

def A073576(n): return sum(sum(d*abs(mobius(d)) for d in divisors(i, generator=True))*A073576(n-i) for i in range(1, n+1))//n if n else 1 # Chai Wah Wu, Aug 23 2024

STATUS

approved

editing

#45 by Vaclav Kotesovec at Sat Mar 31 06:36:16 EDT 2018

STATUS

editing

approved

#44 by Vaclav Kotesovec at Sat Mar 31 06:34:39 EDT 2018

COMMENTS

Euler transform of A008966. - Vaclav Kotesovec, Mar 31 2018

#43 by Vaclav Kotesovec at Sat Mar 31 06:33:32 EDT 2018

MATHEMATICA

nmax = 60; CoefficientList[Series[Exp[Sum[Sum[Abs[MoebiusMu[k]] * x^(j*k) / j, {k, 1, Floor[nmax/j] + 1}], {j, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 31 2018 *)

STATUS

approved

editing

#42 by Vaclav Kotesovec at Sat Mar 24 06:32:07 EDT 2018

STATUS

editing

approved

#41 by Vaclav Kotesovec at Sat Mar 24 06:31:55 EDT 2018

FORMULA

a(n) ~ exp(2*sqrt(n)) / (4*Pi^(3/2)*n^(1/4)). - Vaclav Kotesovec, Mar 24 2018

STATUS

approved

editing

#40 by N. J. A. Sloane at Mon Jun 05 17:33:57 EDT 2017

STATUS

proposed

approved