A257968 Zeroless numbers n such that the product of digits of n, the product of digits of n^2 and the product of digits of n^3 form a geometric progression.
1, 2, 38296, 151373, 398293, 422558, 733381, 971973, 2797318, 3833215, 6988327, 7271256, 8174876, 8732657, 9872323, 9981181, 11617988, 11798921, 14791421, 15376465, 15487926, 15625186, 16549885, 18543639, 21316582, 21492828, 22346329, 22867986, 23373644
Offset: 1
Examples
38296 is in the sequence because the pod equals 2592 (=3*8*2*9*6), pod(38296^2) is 622080, pod(38296^3) is 149299200. 2592*240 = 622080 => 622080*240 = 149299200.
Links
- Giovanni Resta, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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Mathematica
pod[n_]:=Times@@IntegerDigits@n; Select[Range[10^8], pod[#^3] pod[#] == pod[#^2]^2 >0 &] (* Vincenzo Librandi, May 16 2015 *)
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PARI
pod(n) = my(d = digits(n)); prod(k=1, #d, d[k]); isok(n) = (pd = pod(n)) && (pdd = pod(n^2)) && (pdd/pd == pod(n^3)/pdd); \\ Michel Marcus, May 30 2015
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Python
def pod(n): kk = 1 while n > 0: kk= kk*(n%10) n =int(n//10) return kk for i in range (1,10**7): if pod(i**3)*pod(i)==pod(i**2)**2 and pod(i**2)!=0: print (i, pod(i),pod(i**2),pod(i**3),pod(i**2)//pod(i))
Formula
pod(n^3)/pod(n^2)=pod(n^2)/pod(n), where pod(n) = A007954(n).
Extensions
a(17)-a(29) from Giovanni Resta, May 15 2015
Comments