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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.
6
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
Sequence in context: A329562 A069877 A085940 * A189398 A086066 A263327
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