The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A037445

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A037445

Number of infinitary divisors (or i-divisors) of n.
(history; published version)

#81 by Charles R Greathouse IV at Sun Feb 16 08:32:37 EST 2025

LINKS

Eric Weisstein's World of Mathematics, <a href="httphttps://mathworld.wolfram.com/InfinitaryDivisor.html">Infinitary Divisor</a>

Discussion

Sun Feb 16

08:32

OEIS Server: https://oeis.org/edit/global/3014

#80 by Amiram Eldar at Fri Mar 10 13:18:04 EST 2023

STATUS

reviewed

approved

#79 by Michel Marcus at Fri Mar 10 12:44:33 EST 2023

STATUS

proposed

reviewed

#78 by Bernard Schott at Fri Mar 10 04:09:37 EST 2023

STATUS

editing

proposed

#77 by Bernard Schott at Fri Mar 10 04:08:40 EST 2023

FORMULA

a(A037992(n)) = 2^n. - Bernard Schott, Mar 10 2023

CROSSREFS

Cf. A000120, A001316, A004607, A007358, A007357, A037992, A038148, A049417, A064547, A074848, A077609, A124010, A156552, A286575.

STATUS

proposed

editing

Discussion

Fri Mar 10

04:09

Bernard Schott: Added formula + xref.

#76 by Bernard Schott at Thu Mar 09 15:41:30 EST 2023

STATUS

editing

proposed

#75 by Bernard Schott at Thu Mar 09 15:33:13 EST 2023

COMMENTS

The smallest number m with exactly 2^n infinitary divisors is A037992(n); for these values m, a(m) increases also to a new record. - Bernard Schott, Mar 09 2023

CROSSREFS

Cf. A000120, A001316, A004607, A007358, A007357, A037992, A038148, A049417, A064547, A074848, A124010, A156552, A286575.

STATUS

approved

editing

Discussion

Thu Mar 09

15:41

Bernard Schott: Comment.

#74 by Michael De Vlieger at Fri Jul 22 17:45:49 EDT 2022

STATUS

proposed

approved

#73 by Michel Marcus at Fri Jul 22 16:53:06 EDT 2022

STATUS

editing

proposed

#72 by Michel Marcus at Fri Jul 22 16:53:04 EDT 2022

FORMULA

a(n) = productProduct_{k=1..A001221(n)} A000079(A000120(A124010(n,k))): k=1..A001221(n)). - Reinhard Zumkeller, Mar 19 2013

STATUS

proposed

editing