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A066376 Number of "divisors" d < n such that there is another d' < n with d*d' = n. 2

%I

%S 0,1,1,2,1,3,2,3,1,3,1,5,1,5,4,4,1,3,1,5,2,3,1,7,1,3,3,8,1,9,7,5,1,3,

%T 1,5,1,3,1,7,1,5,1,5,3,3,3,9,1,3,3,5,1,7,3,11,1,3,3,14,3,15,13,6,1,3,

%U 1,5,1,3,1,7,2,3,1,5,1,3,1,9,1,3,1,8,4,3,1,7,1,7,3,5,1,7,5,11,1

%N Number of "divisors" d < n such that there is another d' < n with d*d' = n.

%C Define "+" as binary bitwise inclusive-OR and then implement "*" as shift-and-"+". Note that * is commutative and associative and distributes over +.

%H Reinhard Zumkeller, <a href="/A066376/b066376.txt">Table of n, a(n) for n = 1..1000</a>

%e 14 has 5 "divisors": 1, 2, 3, 6, 7, since for example 2*7 = 10*111 = 1110 OR 0000 = 1110; 3*6 = 11*110 = 1100 OR 0110 = 1110.

%o (Haskell)

%o import Data.Bits (Bits, (.|.), shiftL, shiftR)

%o a066376 :: Int -> Int

%o a066376 n = length [d | d <- [1..n-1], any ((== n) . (orm d)) [1..n]] where

%o orm 1 v = v

%o orm u v = orm (shiftR u 1) (shiftL v 1) .|. if odd u then v else 0

%o -- _Reinhard Zumkeller_, Mar 01 2013

%Y Cf. A067139 ("primes").

%K nonn,easy,nice

%O 1,4

%A _Marc LeBrun_, Dec 22 2001

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Last modified November 29 18:41 EST 2021. Contains 349416 sequences. (Running on oeis4.)