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 A095370 Number of distinct prime factors of the repunit (-1 + 10^n)/9. 16
 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; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Factoring certain repunits is especially difficult. REFERENCES 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. LINKS Ray Chandler, Table of n, a(n) for n = 1..322 P. De Geest, Repunits and their prime factors T. Granlund, Repunits. M. Kamada, Factorization of 11...11(Repunits) Y. Koide, Factorization of Repunit Numbers W. M. Snyder, Factoring Repunits, Am. Math. Monthly 89, 462-466, 1982. P. Yiu, Factorizations of repunits R_n for n<=50 Appendix Chap.18.5 pp. 173/360 in 'Recreational Mathematics' FORMULA a(n) = A001221(A002275(n)). EXAMPLE a(62)=5 because 11111111111111111111111111111111111111111111111111111111111111 = 11 * 2791 * 6943319 * 57336415063790604359 * 909090909090909090909090909091. a(97)=3 because (10^97 - 1)/9 = 12004721 * 846035731396919233767211537899097169 * 109399846855370537540339266842070119107662296580348039. MATHEMATICA lst={}; Do[p=(10^n-1)/9; AppendTo[lst, Length[FactorInteger[p]]], {n, 0, 2*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jun 15 2009 *) PROG (PARI) a(n)=omega(10^n\9) \\ Charles R Greathouse IV, Sep 14 2015 CROSSREFS Cf. A067063, A003020, A001221, A002275, A095371. Cf. A046053 (total number of prime factors). Sequence in context: A183413 A183380 A260587 * A046053 A080348 A096396 Adjacent sequences:  A095367 A095368 A095369 * A095371 A095372 A095373 KEYWORD nonn AUTHOR Labos Elemer, Jun 04 2004; corrected Jun 09 2004 STATUS approved

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Last modified September 21 20:01 EDT 2021. Contains 347598 sequences. (Running on oeis4.)