A061509 Write n in decimal, omit 0's, replace the k-th digit d[k] with the k-th prime, raised to d[k]-th power and multiply.

1, 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

Offset: 0

Author

Amarnath Murthy, May 06 2001

Keywords

• base
• less
• nonn

Comments

Not the same as A189398: see formula.

Examples

			a(4) = 2^4 = 16, a(123) = (2^1)*(3^2)*(5^3) = 2250.
For n = 0, the list of nonzero digits is empty, and the empty product equals 1.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 (a(0) = 1 inserted by _M. F. Hasler_, Oct 12 2018)

Crossrefs

Cf. A061510, A000040.

Programs

Haskell

a061509 n = product $ zipWith (^)
  a000040_list (map digitToInt $ filter (/= '0') $ show n)
-- Reinhard Zumkeller, May 03 2011

Mathematica

A061509[n_] := If[n == 0, 1, Times @@ (Prime[Range[Length[#]]]^#) & [DeleteCases[IntegerDigits[n], 0]]];
Array[A061509, 100, 0] (* Paolo Xausa, Nov 26 2024 *)

PARI

A061509(n)=prod(k=1,#n=select(t->t,digits(n)),prime(k)^n[k]) \\ M. F. Hasler, Aug 16 2014

Formula

a(n) = a(n*10^k). a((10^k-1)/9) = primorial(k) = A002110(k).

a(n) = A189398(n) for n <= 100; a(101)=2^1*3^1 = 6 <> A189398(101) = 2^1*3^0*5^1 = 10; a(A052382(n)) = A189398(A052382(n)); a(n) = A000079(A000030(n)) if n has only one nonzero digit; A001221(a(n)) = A055640(n); A001222(a(n)) = A007953(n). - Reinhard Zumkeller, May 03 2011

If n=d[1]d[2]...d[m] in decimal (0M. F. Hasler, Aug 16 2014

A007814(a(n)) = A000030(n). - M. F. Hasler, Aug 18 2014

Extensions

Corrected and extended by Matthew Conroy, May 13 2001

Offset corrected by Reinhard Zumkeller, May 03 2011

Definition corrected by M. F. Hasler, Aug 16 2014

Extended to a(0) = 1 by M. F. Hasler, Oct 12 2018