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A073631
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Nonprimes n such that n divides 3^(n-1)-2^(n-1).
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2
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1, 65, 133, 529, 793, 1105, 1649, 1729, 2059, 2321, 2465, 2701, 2821, 4187, 5185, 6305, 6541, 6601, 6697, 6817, 7471, 7613, 8113, 8911, 10585, 10963, 11521, 13213, 13333, 13427, 14981, 15841, 18721, 19171, 19201, 19909
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Terms 1,65,2059,6305,19171,... are also in A001047
All primes p>3 divide 3^(p-1) - 2^(p-1). It appears that a(1) = 1 and a(4) = 529 = 23^2 are the only perfect squares in a(n). Most terms of a(n) are squarefree. First 50 non-squarefree terms of a(n) are the multiples of 23^2. Conjecture: All non-squarefree terms of a(n) are the multiples of 23^2. Numbers n such that k=n*23^2 divides 3^(k-1) - 2^(k-1) are listed in A130058 = {1,67,89,133,199,331,617,793,881,5281,8911,1419,13333,...}. - Alexander Adamchuk (alex(AT)kolmogorov.com), May 04 2007
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CROSSREFS
| Cf. A001047.
Cf. A001047 = 3^n - 2^n. Cf. A038876, A097934 = Primes p such that p divides 3^((p-1)/2) - 2^((p-1)/2). Cf. A130059, A130058 = numbers n such that k=n*23^2 divides 3^(k-1) - 2^(k-1).
Sequence in context: A044188 A044569 A158071 * A194002 A092226 A121944
Adjacent sequences: A073628 A073629 A073630 * A073632 A073633 A073634
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KEYWORD
| easy,nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 29 2002
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