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A175066
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a(1) = 1, for n >= 2: a(n) = number of ways h to write perfect powers A117453(n) as m^k (m >= 2, k >= 2).
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6
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1, 2, 3, 2, 3, 2, 2, 3, 3, 2, 2, 5, 3, 2, 2, 3, 3, 2, 2, 2, 3, 2, 3, 2, 3, 4, 2, 2, 3, 2, 2, 2, 2, 5, 2, 2, 3, 2, 5, 2, 2, 2, 2, 3, 5, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 3, 3, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 7, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2
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OFFSET
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1,2
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COMMENTS
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Perfect powers with first occurrence of h >= 2: 16, 64, 65536, 4096, ... (A175065)
a(n) for n>1 is the subsequence of A253642 formed by the terms which exceed 1; equivalently, a(n)+1 for n>1 is the subsequence of A175064 formed by the terms which exceed 2. Also, sum of a(n)-1 over such n that A117453(n)<10^m gives A275358(m). - Andrey Zabolotskiy, Aug 16 2016
Numbers n such that a(n) is nonprime are 1, 26, 110, ... - Altug Alkan, Aug 22 2016
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LINKS
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FORMULA
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EXAMPLE
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For n = 12, A117453(12) = 4096 and a(12)=5 since there are 5 ways to write 4096 as m^k: 64^2 = 16^3 = 8^4 = 4^6 = 2^12.
729=27^2=9^3=3^6 and 1024=32^2=4^5=2^10 yield a(8)=a(9)=3. - R. J. Mathar, Jan 24 2010
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PROG
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(PARI) lista(nn) = {print1(1, ", "); for (i=2, nn, if (po = ispower(i), np = sum(j=2, po, ispower(i, j)); if (np>1, print1(np, ", ")); ); ); } \\ Michel Marcus, Mar 20 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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