A081318 -id:A081318 - cp's OEIS frontend

A057951 Number of prime factors of 10^n - 1 (counted with multiplicity).

2, 3, 4, 4, 4, 7, 4, 6, 6, 6, 4, 9, 5, 6, 8, 8, 4, 11, 3, 9, 9, 9, 3, 12, 7, 8, 9, 10, 7, 15, 5, 13, 8, 8, 9, 14, 5, 5, 8, 13, 6, 17, 6, 13, 12, 8, 4, 15, 6, 12, 10, 11, 6, 16, 10, 14, 8, 10, 4, 22, 9, 7, 16, 17, 9, 17, 5, 12, 8, 14, 4, 20, 5, 9, 14, 8, 10, 18

Offset: 1

Patrick De Geest, Nov 15 2000

nonn

Max Alekseyev, Table of n, a(n) for n = 1..352 (first 322 terms from Ray Chandler)
Makoto Kamada, Factorizations of 11...11 (Repunit).
S. S. Wagstaff, Jr., Main Tables from the Cunningham Project.
S. S. Wagstaff, Jr., The Cunningham Project

bigomega(b^n-1): this sequence (b=10), A057952 (b=9), A057953 (b=8), A057954 (b=7), A057955 (b=6), A057956 (b=5), A057957 (b=4), A057958 (b=3), A046051 (b=2).

Cf. A001222, A002283, A046053, A085035, A003020, A046107, A005422, A061075, A102380, A095370, A147556, A081317, A081318, A102347, A112505.

PrimeOmega[10^Range[70]-1] (* Jayanta Basu, May 29 2013 *)

a(n)=bigomega(10^n-1) \\ Charles R Greathouse IV, Sep 14 2015

Mobius transform of A085035 - T. D. Noe, Jun 19 2003
a(n) = Omega(10^n -1) = Omega(R_n) + 2 = A046053(n) + 2 {where Omega(n) = A001222(n) and R_n = (10^n - 1)/9 = A002275(n)}. - Lekraj Beedassy, Jun 09 2006
a(n) = A001222(A002283(n)). - Ray Chandler, Apr 22 2017

Erroneous b-file replaced by Ray Chandler, Apr 26 2017

A102146 a(n) = sigma(10^n - 1), where sigma(n) is the sum of positive divisors of n.

Original entry on oeis.org

13, 156, 1520, 15912, 148512, 2042880, 14508000, 162493344, 1534205464, 16203253248, 144451398000, 2063316971520, 14903272088640, 158269280832000, 1614847741624320, 17205180696931968, 144444514193267496

Offset: 1

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Feb 14 2005

nonn

Max Alekseyev, Table of n, a(n) for n = 1..352 (terms 1..322 from Ray Chandler)
C. Caldwell, Sigma function.

Cf. A000203, A001270, A002283, A003020, A005422, A046053, A046107, A046412, A046415, A046416, A046417, A046418, A046419, A046420, A057951, A059892, A061075, A070528, A070529, A081317, A081318, A085035, A095370, A095413, A095414, A095417, A095418, A102347, A102380, A112505, A147556, A295503, A366669.

DivisorSigma[1,10^Range[20]-1] (* Harvey P. Dale, Jan 05 2012 *)

a(n) = sigma(10^n-1); \\ Michel Marcus, Apr 22 2017

a(n) = A000203(A002283(n)). - Ray Chandler, Apr 22 2017

A081317 Primes p such that p divides 10^n-1, p is the largest prime producing decimal fraction period n and p is not the largest prime dividing 10^n-1.

Original entry on oeis.org

13, 52579, 8779, 2161, 69857, 909090909090909091, 459691, 549797184491917, 14175966169, 183411838171, 296557347313446299, 388847808493, 3404193829806058997303, 8985695684401, 297262705009139006771611927

Offset: 1

Hugo Pfoertner, Mar 18 2003

			a(1)=13 because the largest factor 37 in the factorization of 10^6-1=999999=3^3*7*11*13*37 already occurs in the factorization of 10^3-1=3^3*37 and produces only a decimal fraction period of 3. 1/37=0.027027027...., 1/13=0.0769230769230...

Max Alekseyev, Table of n, a(n) for n = 1..54 (first 50 terms from Ray Chandler)
Sam Wagstaff, The Cunningham Project, The Main Tables

Cf. A005422, A003020, A061075, A081318.

Numbers in A061075(n) such that A061075(n) is not equal to A005422(n). The corresponding values of n are given in A081318.

a(n) = A061075(A081318(n)). - Max Alekseyev, Apr 27 2022

More terms from Hans Havermann, May 31 2003

cp's OEIS Frontend

A057951 Number of prime factors of 10^n - 1 (counted with multiplicity).

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A102146 a(n) = sigma(10^n - 1), where sigma(n) is the sum of positive divisors of n.

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A081317 Primes p such that p divides 10^n-1, p is the largest prime producing decimal fraction period n and p is not the largest prime dividing 10^n-1.

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