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A054842 If n = a + 10 * b + 100 * c + 1000 * d + ... then a(n) = (2^a) * (3^b) * (5^c) * (7^d) * ... 14

%I

%S 1,2,4,8,16,32,64,128,256,512,3,6,12,24,48,96,192,384,768,1536,9,18,

%T 36,72,144,288,576,1152,2304,4608,27,54,108,216,432,864,1728,3456,

%U 6912,13824,81,162,324,648,1296,2592,5184,10368,20736,41472,243,486,972

%N If n = a + 10 * b + 100 * c + 1000 * d + ... then a(n) = (2^a) * (3^b) * (5^c) * (7^d) * ...

%C a((10^k-1)/9) = Primorial(k)= A061509((10^k-1)/9). This is a rearrangement of whole numbers. a(m) = a(n) iff m = n. (Unlike A061509, in which a(n) = a(n*10^k)).) - _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jul 14 2003

%C Part of the previous comment is incorrect: as a set, this sequence consists of numbers n such that the largest exponent appearing in the prime factorization of n is 9. So this cannot be a rearrangement (or permutation) of the natural numbers. - _Tom Edgar_, Oct 20 2015

%H R. Zumkeller, <a href="/A054842/b054842.txt">Table of n, a(n) for n = 0..9999</a>

%F a(n) = f(n, 1, 1) with f(x, y, z) = if x > 0 then f(floor(x/10), y*prime(z)^(x mod 10), z+1) else y. - _Reinhard Zumkeller_, Mar 13 2010

%e a(15)=96 because 3^1 * 2^5 = 3*32 = 96.

%o (Haskell)

%o a054842 = f a000040_list 1 where

%o f _ y 0 = y

%o f (p:ps) y x = f ps (y * p ^ d) x' where (x', d) = divMod x 10

%o -- _Reinhard Zumkeller_, Aug 03 2015

%Y Cf. A054841, A085840.

%Y Cf. A019565, A101278. - _Reinhard Zumkeller_, Mar 13 2010

%K base,nonn,look

%O 0,2

%A _Henry Bottomley_, Apr 11 2000

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Last modified June 18 07:06 EDT 2019. Contains 324203 sequences. (Running on oeis4.)