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A189398 a(n) = 2^d(1) * 3^d(2) * ... * prime(k)^d(k), where d(1)d(2)...d(k) is the decimal representation of n. 6
2, 4, 8, 16, 32, 64, 128, 256, 512, 2, 6, 18, 54, 162, 486, 1458, 4374, 13122, 39366, 4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78732, 8, 24, 72, 216, 648, 1944, 5832, 17496, 52488, 157464, 16, 48, 144, 432, 1296, 3888, 11664, 34992, 104976, 314928, 32 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Not the same as A061509: a(n) = A061509(n) for n <= 100; a(101)=2^1*3^0*5^1=10 <> A061509(101)=2^1*3^1=6;

a(A052382(n)) = A000079(A000030(a052382(n))) = A061509(A052382(n));

a(A002275(n)) = A002110(n): a(n-th rep-unit) = n-th primorial;

a(n*A011557(k)) = a(n): trailing zeros don't matter;

A001221(a(n)) = A055640(n): number of distinct prime factors of a(n) = number of nonzero digits of n;

A001222(a(n)) = A007953(n): number of all prime factors of a(n) = sum of digits of n;

a(81312000) = 2^8*3^1*5^3*7^1*11^2*13^0*17^0*19^0 = 81312000, the smallest fixed point, is called the Meertens number.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Richard S. Bird, Functional Pearl: Meertens number, Journal of Functional Programming 8 (1), Jan 1998, 83-88.

Wikipedia, Meertens number

MAPLE

a:= n-> `if`(n=0, 1, ithprime(length(n))^irem(n, 10, 'm') *a(m)):

seq(a(n), n=1..110);  # Alois P. Heinz, May 04 2011

MATHEMATICA

a[n_] := (p = Prime[Range[Length[d = IntegerDigits[n]]]]; Times @@ (p^d)); Array[a, 50] (* Jean-Fran├žois Alcover, Jan 09 2016 *)

PROG

(Haskell)

import Data.Char (digitToInt)

import Data.List (findIndices)

a189398 n = product $ zipWith (^) a000040_list (map digitToInt $ show n)

-- Two computations of the Meertens number: the first is brute force,

meertens = map succ $ findIndices (\x -> a189398 x == x) [1..]

-- ... and the second is more efficient, from Bird reference, page 87:

meertens' k = [n | (n, g) <- candidates (0, 1), n == g] where

  candidates        = concat . map (search pps) . tail . labels ps

  ps : pps          = map (\p -> iterate (p *) 1) $ take k a000040_list

  search [] x       = [x]

  search (ps:pps) x = x : concat (map (search pps) (labels ps x))

  labels ps (n, g)   = zip (map (10*n +) [0..9]) (chop $ map (g *) ps)

  chop              = takeWhile (< 10^k)

-- Time and space required, GHC interpreted, Mac OS X, 2.66 GHz:

-- for >head meertens: (466.87 secs, 254780027728 bytes);

-- for >meertens' 8:   (  0.28 secs,     62027124 bytes).

(PARI) a(n)=my(d=digits(n), p=primes(#d)); prod(i=1, #d, p[i]^d[i]) \\ Charles R Greathouse IV, Aug 19 2014

(Python)

from sympy import prime

from operator import mul

from functools import reduce

def A189398(n):

....return reduce(mul, (prime(i)**int(d) for i, d in enumerate(str(n), start=1)))

# implementation using recursion

def _A189398(n):

....nlen = len(n)

....return _A189398(n[:-1])*prime(nlen)**int(n[-1]) if nlen > 1 else 2**int(n)

def A189398(n):

....return _A189398(str(n))

# Chai Wah Wu, Aug 31 2014

CROSSREFS

Cf. A000040.

Sequence in context: A069877 A085940 A061509 * A086066 A263327 A085941

Adjacent sequences:  A189395 A189396 A189397 * A189399 A189400 A189401

KEYWORD

nonn,base,look

AUTHOR

Reinhard Zumkeller, May 03 2011

STATUS

approved

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Last modified December 9 13:48 EST 2016. Contains 278971 sequences.