The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A174903 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A174903

Number of divisors d of n such that d<e<2*d for at least another divisor e of n.
(history; published version)

#11 by Michel Marcus at Sat Apr 13 05:12:53 EDT 2024

STATUS

reviewed

approved

#10 by Joerg Arndt at Sat Apr 13 04:31:18 EDT 2024

STATUS

proposed

reviewed

#9 by Amiram Eldar at Sat Apr 13 04:12:48 EDT 2024

STATUS

editing

proposed

#8 by Amiram Eldar at Sat Apr 13 04:01:40 EDT 2024

FORMULA

a(m)*a(n) <= a(m)*a(n) for m, n coprime.

#7 by Amiram Eldar at Sat Apr 13 04:01:27 EDT 2024

COMMENTS

a(A174905(n)) = 0; a(A005279(n)) > 0;

a(A174904(n)) = n and a(m) <> n for m < A174904(n);

a(m)*a(n) <= a(m)*a(n) for m, n coprime.

LINKS

R. Reinhard Zumkeller, <a href="/A174903/b174903.txt">Table of n, a(n) for n = 1..10000</a>

FORMULA

a(A174905(n)) = 0; a(A005279(n)) > 0.

a(A174904(n)) = n and a(m) <> n for m < A174904(n).

a(m)*a(n) <= a(m)*a(n) for m, n coprime.

#6 by Amiram Eldar at Sat Apr 13 04:00:57 EDT 2024

MATHEMATICA

a[n_] := Module[{d = Divisors[n]}, Count[d, _?(Length[Intersection[Range[# + 1, 2*# - 1], d]] > 0 &)]]; Array[a, 100] (* Amiram Eldar, Apr 13 2024 *)

STATUS

approved

editing

#5 by Reinhard Zumkeller at Mon Sep 29 02:28:19 EDT 2014

STATUS

editing

approved

#4 by Reinhard Zumkeller at Mon Sep 29 01:40:27 EDT 2014

PROG

(Haskell)

import Data.List (intersect)

a174903 n = length [d | let ds = a027750_row n, d <- ds,

not $ null [e | e <- [d+1 .. 2*d-1] `intersect` ds]]

-- Reinhard Zumkeller, Sep 29 2014

CROSSREFS

Cf. A000005, A005279, A174904, A174905.

STATUS

approved

editing

#3 by Russ Cox at Fri Mar 30 18:51:05 EDT 2012

AUTHOR

_Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), _, Apr 01 2010

Discussion

Fri Mar 30

18:51

OEIS Server: https://oeis.org/edit/global/246

#2 by N. J. A. Sloane at Thu Nov 11 07:34:06 EST 2010

LINKS

R. Zumkeller, <a href="/A174903/b174903.txt">Table of n, a(n) for n = 1..10000</a>

KEYWORD

nonn,new

nonn