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

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 9, 18, 36, 72, 144, 288, 576, 1152, 2304, 4608, 27, 54, 108, 216, 432, 864, 1728, 3456, 6912, 13824, 81, 162, 324, 648, 1296, 2592, 5184, 10368, 20736, 41472, 243, 486, 972, 1944

Offset

0,2

Comments

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

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

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..9999

Formula

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

Example

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

Mathematica

A054842[n_] := Times @@ (Prime[Range[Length[#], 1, -1]]^#) & [IntegerDigits[n]];
Array[A054842, 100, 0] (* Paolo Xausa, Nov 25 2024 *)

Prog

(Haskell)
a054842 = f a000040_list 1 where
   f _      y 0 = y
   f (p:ps) y x = f ps (y * p ^ d) x'  where (x', d) = divMod x 10
-- Reinhard Zumkeller, Aug 03 2015
(PARI) a(n)= my(d=Vecrev(digits(n))); factorback(primes(#d), d); \\ Ruud H.G. van Tol, Nov 28 2024

Crossrefs

Cf. A054841, A069877, A085840.

Cf. analogous sequences for other bases: A019565 (base 2), A101278 (base 3), A101942 (base 4), A101943 (base 5), A276076 (factorial base), A276086 (primorial base).

Sequence in context: A086066 A263327 A085941 * A290389 A101440 A126605

Adjacent sequences: A054839 A054840 A054841 * A054843 A054844 A054845

Keyword

base,nonn,easy,look

Author

Henry Bottomley, Apr 11 2000

Status

approved