cp's OEIS Frontend

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.

%I A061509 #36 Nov 26 2024 09:56:07
%S A061509 1,2,4,8,16,32,64,128,256,512,2,6,18,54,162,486,1458,4374,13122,39366,
%T A061509 4,12,36,108,324,972,2916,8748,26244,78732,8,24,72,216,648,1944,5832,
%U A061509 17496,52488,157464,16,48,144,432,1296,3888,11664,34992,104976,314928
%N 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.
%C A061509 Not the same as A189398: see formula.
%H A061509 Reinhard Zumkeller, <a href="/A061509/b061509.txt">Table of n, a(n) for n = 0..10000</a> (a(0) = 1 inserted by _M. F. Hasler_, Oct 12 2018)
%F A061509 a(n) = a(n*10^k). a((10^k-1)/9) = primorial(k) = A002110(k).
%F A061509 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
%F A061509 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
%F A061509 A007814(a(n)) = A000030(n). - _M. F. Hasler_, Aug 18 2014
%e A061509 a(4) = 2^4 = 16, a(123) = (2^1)*(3^2)*(5^3) = 2250.
%e A061509 For n = 0, the list of nonzero digits is empty, and the empty product equals 1.
%t A061509 A061509[n_] := If[n == 0, 1, Times @@ (Prime[Range[Length[#]]]^#) & [DeleteCases[IntegerDigits[n], 0]]];
%t A061509 Array[A061509, 100, 0] (* _Paolo Xausa_, Nov 26 2024 *)
%o A061509 (Haskell)
%o A061509 a061509 n = product $ zipWith (^)
%o A061509   a000040_list (map digitToInt $ filter (/= '0') $ show n)
%o A061509 -- _Reinhard Zumkeller_, May 03 2011
%o A061509 (PARI) A061509(n)=prod(k=1,#n=select(t->t,digits(n)),prime(k)^n[k]) \\ _M. F. Hasler_, Aug 16 2014
%Y A061509 Cf. A061510, A000040.
%K A061509 base,less,nonn
%O A061509 0,2
%A A061509 _Amarnath Murthy_, May 06 2001
%E A061509 Corrected and extended by _Matthew Conroy_, May 13 2001
%E A061509 Offset corrected by _Reinhard Zumkeller_, May 03 2011
%E A061509 Definition corrected by _M. F. Hasler_, Aug 16 2014
%E A061509 Extended to a(0) = 1 by _M. F. Hasler_, Oct 12 2018