The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A374930 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A374930

Expansion of Sum_{1<=i<=j<=k} q^(i+j+k)/( (1-q^i)*(1-q^j)*(1-q^k) )^2.
(history; published version)

#20 by Michel Marcus at Thu Jul 25 02:48:34 EDT 2024

STATUS

reviewed

approved

#19 by Joerg Arndt at Thu Jul 25 00:52:52 EDT 2024

STATUS

proposed

reviewed

#18 by Chai Wah Wu at Wed Jul 24 23:15:16 EDT 2024

STATUS

editing

proposed

#17 by Chai Wah Wu at Wed Jul 24 23:15:11 EDT 2024

PROG

return (31*prod((p**(5*(e+1))-1)//(p**5-1) for p, e in f)-70*(n+1)*prod((p**(3*(e+1))-1)//(p**3-1) for p, e in f) + (20*n*((n<<1)+3)+9)*prod((p**(e+1)-1)//(p-1) for p, e in f))//1920 # Chai Wah Wu, Jul 24 2024

#16 by Chai Wah Wu at Wed Jul 24 23:15:00 EDT 2024

PROG

(Python)

from math import prod

from sympy import factorint

def A374930(n):

f = factorint(n).items()

STATUS

approved

editing

#15 by Michael De Vlieger at Wed Jul 24 13:22:20 EDT 2024

STATUS

reviewed

approved

#14 by Amiram Eldar at Wed Jul 24 11:40:21 EDT 2024

STATUS

proposed

reviewed

#13 by Paolo Xausa at Wed Jul 24 09:56:18 EDT 2024

STATUS

editing

proposed

#12 by Paolo Xausa at Wed Jul 24 09:55:38 EDT 2024

MATHEMATICA

A374930[n_] := (31*DivisorSigma[5, n] - 70*(n + 1)*DivisorSigma[3, n] + (40*n^2 + 60*n + 9)*DivisorSigma[1, n])/1920; Array[A374930, 50, 3] (* _Paolo Xausa_, Jul 24 2024 *)

Array[A374930, 50, 3] (* Paolo Xausa, Jul 24 2024 *)

#11 by Paolo Xausa at Wed Jul 24 09:55:24 EDT 2024

MATHEMATICA

A374930[n_] := (31*DivisorSigma[5, n] - 70*(n + 1)*DivisorSigma[3, n] + (40*n^2 + 60*n + 9)*DivisorSigma[1, n])/1920; Array[A374930, 50, 3] (* Paolo Xausa, Jul 24 2024 *)

STATUS

approved

editing