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

0,2

Comments

Not the same as A189398: see formula.

Links

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

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 (0<d[k]<10: m nonzero digits), then a(n)=p[1]^d[1]*...*p[m]^d[m], where p[k] is the k-th prime. - M. F. Hasler, Aug 16 2014

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

Example

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.

Prog

(Haskell)
a061509 n = product $ zipWith (^)
  a000040_list (map digitToInt $ filter (/= '0') $ show n)
-- Reinhard Zumkeller, May 03 2011
(PARI) A061509(n)=prod(k=1, #n=select(t->t, digits(n)), prime(k)^n[k]) \\ M. F. Hasler, Aug 16 2014

Crossrefs

Cf. A061510, A000040.

Sequence in context: A329562 A069877 A085940 * A189398 A086066 A263327

Adjacent sequences: A061506 A061507 A061508 * A061510 A061511 A061512

Keyword

base,less,nonn

Author

Amarnath Murthy, May 06 2001

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

Status

approved