The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A143128

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A143128

a(n) = Sum_{k=1..n} k*sigma(k).
(history; published version)

#61 by Alois P. Heinz at Sat Oct 21 17:07:00 EDT 2023

STATUS

proposed

approved

#60 by Chai Wah Wu at Sat Oct 21 15:57:45 EDT 2023

STATUS

editing

proposed

#59 by Chai Wah Wu at Sat Oct 21 15:57:42 EDT 2023

PROG

(Python)

from math import isqrt

def A143128(n): return ((-((s:=isqrt(n))*(s+1))**2*(2*s+1)>>1) + sum((q:=n//k)*(q+1)*k*(3*k+2*q+1) for k in range(1, s+1)))//6 # Chai Wah Wu, Oct 21 2023

STATUS

approved

editing

#58 by Joerg Arndt at Sat Oct 21 01:25:52 EDT 2023

STATUS

reviewed

approved

#57 by Michel Marcus at Sat Oct 21 01:25:25 EDT 2023

STATUS

proposed

reviewed

#56 by Chai Wah Wu at Fri Oct 20 17:28:07 EDT 2023

STATUS

editing

proposed

#55 by Chai Wah Wu at Fri Oct 20 17:28:00 EDT 2023

PROG

(Python)

def A143128(n): return sum(k**2*(m:=n//k)*(m+1)>>1 for k in range(1, n+1)) # Chai Wah Wu, Oct 20 2023

STATUS

approved

editing

#54 by Charles R Greathouse IV at Thu Sep 08 08:45:37 EDT 2022

PROG

(MAGMAMagma) [(&+[k*DivisorSigma(1, k): k in [1..n]]): n in [1..50]]; // G. C. Greubel, Nov 21 2018

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#53 by Peter Luschny at Fri Nov 27 11:04:37 EST 2020

STATUS

reviewed

approved

#52 by Michel Marcus at Fri Nov 27 00:01:02 EST 2020

STATUS

proposed

reviewed