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Search: id:A134194
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| A134194 |
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a(n) = the smallest positive divisor of n that does not occur among the exponents in the prime-factorization of n. |
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1
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| 1, 2, 3, 1, 5, 2, 7, 1, 1, 2, 11, 3, 13, 2, 3, 1, 17, 3, 19, 4, 3, 2, 23, 2, 1, 2, 1, 4, 29, 2, 31, 1, 3, 2, 5, 1, 37, 2, 3, 2, 41, 2, 43, 4, 3, 2, 47, 2, 1, 5, 3, 4, 53, 2, 5, 2, 3, 2, 59, 3, 61, 2, 3, 1, 5, 2, 67, 4, 3, 2, 71, 1, 73, 2, 3, 4, 7, 2, 79, 2, 1, 2, 83, 3, 5, 2, 3, 2, 89, 3, 7, 4, 3, 2, 5, 2
(list; graph; listen)
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OFFSET
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1,2
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EXAMPLE
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The prime factorization of 24 is 2^3 * 3^1. The exponents are 3 and 1. The positive divisors of 24 are 1,2,3,4,6,8,12,24. Therefore since only the divisors 1 and 3 occur among the exponents in the prime-factorization of 24, then a(24) = 2 is the smallest divisor not occurring among those exponents.
The prime factorization of 40 is 2^3 * 5^1. The exponents are 3 and 1. The positive divisors of 40 are 1,2,4,5,8,10,20,40. Therefore since only the divisor 1 occurs among the exponents in the prime-factorization of 40, then a(40) = 2 is the smallest divisor not occurring among those exponents.
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MATHEMATICA
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Table[Min[Complement[Divisors[n], Table[FactorInteger[n][[i, 2]], {i, 1, Length[FactorInteger[n]]}]]], {n, 1, 80}] [From Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Aug 30 2008]
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CROSSREFS
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Sequence in context: A021816 A055023 A126773 this_sequence A086112 A138798 A134734
Adjacent sequences: A134191 A134192 A134193 this_sequence A134195 A134196 A134197
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), Jan 13 2008
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EXTENSIONS
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Corrected and extended by Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Aug 30 2008
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