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Search: id:A089363
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| A089363 |
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Numbers of pairs (i, j), i, j > 1, such that i^j <= 10^n. |
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+0
1
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| 3, 16, 50, 145, 407, 1177, 3508, 10677, 32967, 102719, 321798, 1011538, 3186390, 10050746, 31730137, 100228044, 316713624, 1001037551, 3164497350, 10004755379, 31632975601, 100021893197, 316274794667, 1000101078155
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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These numbers are related to the divergent series r sum(n^(1/k) = n^1/2 + n^1/3 + ...n^1/r for abs(n) > 0 and r=sqrt(n). k=2
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FORMULA
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a(n) = A089361(10^n) = sum_{p = 2..inf} [floor(10^(n/p)) - 1]. - David Wasserman (wasserma(AT)spawar.navy.mil), Sep 14 2005
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EXAMPLE
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There are 16 perfect powers <= 100: 2^2, 2^3, 3^2, 2^4, 4^2, 5^2, 3^3, 2^5, 6^2, 7^2, 2^6, 4^3, 8^2, 3^4, 9^2, 10^2
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PROGRAM
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(PARI) plessn10(n, m) = { for(k=1, n, s=0; z = 10^k; r = floor(sqrt(z)); for(x=m, r, for(y=2, r, p = floor(x^y); if(p<=z, s++) ) ); print1(s", ") ) }
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CROSSREFS
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Adjacent sequences: A089360 A089361 A089362 this_sequence A089364 A089365 A089366
Sequence in context: A081270 A092466 A004320 this_sequence A000574 A041233 A055194
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Dec 27 2003
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Sep 14 2005
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