cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

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

Views

Author

Patrick De Geest, Nov 15 2000

Keywords

Links

Crossrefs

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.

Programs

Formula

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

Extensions

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

Views

Author

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

Keywords

Links

Crossrefs

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.

Programs

  • Mathematica
    DivisorSigma[1,10^Range[20]-1] (* Harvey P. Dale, Jan 05 2012 *)
  • PARI
    a(n) = sigma(10^n-1); \\ Michel Marcus, Apr 22 2017

Formula

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

A147555 Smallest prime factor of prime(n)-th repunit number.

Original entry on oeis.org

11, 3, 41, 239, 21649, 53, 2071723, 1111111111111111111, 11111111111111111111111, 3191, 2791, 2028119, 83, 173, 35121409, 107, 2559647034361, 733, 493121, 241573142393627673576957439049, 12171337159
Offset: 1

Views

Author

Farideh Firoozbakht, Dec 26 2008

Keywords

Comments

The sequence of repunit primes is a subsequence of this sequence.

Examples

			prime(15)=47 and (10^47-1)/9 = 35121409*316362908763458525001406154038726382279, so a(15)=35121409.

Links

Crossrefs

Cf. A000040, A002275, A004022, A019328, A020639, A067063, A147556.

Formula

a(n) = A067063(A000040(n)) = A020639(A002275(A000040(n))) = A020639(A019328(A000040(n))). - Ray Chandler, May 11 2017

Extensions

Edited by Ray Chandler, Apr 06 2011
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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