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 A175066 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). 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Perfect powers with first occurrence of h >= 2: 16, 64, 65536, 4096, ... LINKS EXAMPLE For n = 12; A117453 (12) = 5; 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. [From R. J. Mathar, Jan 24 2010] PROG (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 CROSSREFS Sequence in context: A214323 A121549 A023397 * A066102 A036048 A145384 Adjacent sequences:  A175063 A175064 A175065 * A175067 A175068 A175069 KEYWORD nonn AUTHOR Jaroslav Krizek, Jan 23 2010 EXTENSIONS Corrected and extended by R. J. Mathar, Jan 24 2010 STATUS approved

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