The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A327329

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A327329

Twice the sum of all divisors of all positive integers <= n.
(history; published version)

#59 by N. J. A. Sloane at Sun Oct 22 16:36:55 EDT 2023

STATUS

proposed

approved

#58 by Chai Wah Wu at Sun Oct 22 15:18:05 EDT 2023

STATUS

editing

proposed

#57 by Chai Wah Wu at Sun Oct 22 15:18:02 EDT 2023

PROG

(Python)

from math import isqrt

def A327329(n): return -(s:=isqrt(n))**2*(s+1)+sum((q:=n//k)*((k<<1)+q+1) for k in range(1, s+1)) # Chai Wah Wu, Oct 22 2023

STATUS

approved

editing

#56 by N. J. A. Sloane at Mon Dec 20 18:48:22 EST 2021

STATUS

proposed

approved

#55 by Michel Marcus at Mon Dec 20 09:05:10 EST 2021

STATUS

editing

proposed

#54 by Michel Marcus at Mon Dec 20 09:05:01 EST 2021

PROG

(PARI) a(n) = 2*sum(k=1, n, sigma(k)); \\ Michel Marcus, Dec 20 2021

STATUS

proposed

editing

#53 by Omar E. Pol at Sat Dec 18 21:48:30 EST 2021

STATUS

editing

proposed

#52 by Omar E. Pol at Sat Dec 18 21:48:26 EST 2021

CROSSREFS

Cf. A001105, A006218, A013661, A024916, A067436, A222548, A236104, A237591, A237593, A243980, A245092, A262626.

STATUS

proposed

editing

#51 by Jon E. Schoenfield at Thu Dec 16 23:54:53 EST 2021

STATUS

editing

proposed

#50 by Jon E. Schoenfield at Thu Dec 16 23:54:50 EST 2021

COMMENTS

a(n) is also the total area of the horizontal faces in the stepped pyramid with n levels described in A245092, (that is the total area of the terraces plus the area of the base). - Omar E. Pol, Dec 15 2021

STATUS

proposed

editing