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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
This sequence appears to be infinite.
LINKS
FORMULA
pod(n^3)/pod(n^2)=pod(n^2)/pod(n), where pod(n) = A007954(n).
EXAMPLE
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.
MATHEMATICA
pod[n_]:=Times@@IntegerDigits@n; Select[Range[10^8], pod[#^3] pod[#] == pod[#^2]^2 >0 &] (* Vincenzo Librandi, May 16 2015 *)
PROG
(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))
(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
CROSSREFS
Cf. A052382 (zeroless numbers), A007954 (product of digits).
Sequence in context: A330304 A272166 A291881 * A303738 A055578 A232733
KEYWORD
nonn,base
AUTHOR
Pieter Post, May 15 2015
EXTENSIONS
a(17)-a(29) from Giovanni Resta, May 15 2015
STATUS
approved

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Last modified May 27 16:57 EDT 2024. Contains 372880 sequences. (Running on oeis4.)