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Search: id:A095370
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| A095370 |
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Number of distinct prime factors of the repunit (-1+10^n)/9. |
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+0
11
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| 0, 1, 2, 2, 2, 5, 2, 4, 3, 4, 2, 7, 3, 4, 6, 6, 2, 8, 1, 7, 7, 6, 1, 10, 5, 6, 5, 8, 5, 13, 3, 11, 6, 6, 7, 11, 3, 3, 6, 11, 4, 14, 4, 10, 9, 6, 2, 13, 4, 10, 8, 9, 4, 12, 8, 12, 6, 8, 2, 20, 7, 5, 13, 15, 7, 14, 3, 10, 6, 12, 2, 17, 3, 7, 12, 6, 8, 15, 6, 15, 10, 7, 3, 21, 7, 8, 10, 14, 5, 21, 12, 10
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Factoring certain repunits is especially difficult.
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REFERENCES
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Snyder, W. M. "Factoring Repunits." Am. Math. Monthly 89, 462-466, 1982.
Yates, S. "Peculiar Properties of Repunits." J. Recr. Math. 2, 139-146,1969.
Yates, S. "Prime Divisors of Repunits." J. Recr. Math. 8, 33-38, 1975.
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LINKS
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P. De Geest, Repunits and their prime factors
T. Granlund, Repunits.
M. Kamada, Factorization of 11...11(Repunits)
Y. Koide, Factorization of Repunit Numbers
P. Yiu, Factorizations of repunits R_n for n=<50 Appendix Chap.18.5 pp. 173/360 in 'Recreational Mathematics'
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FORMULA
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a[n]=A001221[A002275(n)]
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EXAMPLE
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a[62]=5 because
11111111111111111111111111111111111111111111111111111111111111=
11*2791*6943319*57336415063790604359*909090909090909090909090909091
a[97]=3 because (10^97-1)/9=12004721*846035731396919233767211537899097169*109399846855370537540339266842070119107662296580348039.
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MATHEMATICA
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lst={}; Do[p=(10^n-1)/9; AppendTo[lst, Length[FactorInteger[p]]], {n, 0, 2*4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 15 2009]
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CROSSREFS
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Cf. A067063, A003020, A001221, A002275, A094371.
Cf. A046053 (total number of prime factors).
Sequence in context: A130155 A113516 A120642 this_sequence A046053 A080348 A096396
Adjacent sequences: A095367 A095368 A095369 this_sequence A095371 A095372 A095373
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jun 04 2004; corrected Jun 09 2004
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