A085035 -id:A085035 - cp's OEIS frontend

A085034 Number of prime factors of cyclotomic(n,9), which is A019327(n), the value of the n-th cyclotomic polynomial evaluated at x=9.

3, 2, 2, 2, 3, 1, 2, 3, 3, 2, 4, 1, 2, 2, 3, 2, 5, 1, 4, 1, 4, 2, 3, 3, 4, 2, 5, 2, 6, 1, 5, 2, 3, 2, 3, 1, 5, 2, 8, 2, 5, 2, 3, 3, 5, 2, 7, 2, 7, 4, 5, 2, 5, 1, 5, 3, 6, 2, 4, 3, 4, 3, 5, 2, 4, 1, 5, 3, 7, 3, 6, 2, 6, 3, 7, 4, 4, 2

Offset: 1

T. D. Noe, Jun 19 2003

nonn

The Mobius transform of this sequence yields A057952, number of prime factors of 9^n-1.

See references at A085021

Max Alekseyev, Table of n, a(n) for n = 1..690

omega(Phi(n,x)): A085021 (x=2), A085028 (x=3), A085029 (x=4), A085030 (x=5), A085031 (x=6), A085032 (x=7), A085033 (x=8), this sequence (x=9), A085035 (x=10).

Cf. A019327, A057952, A059891, A274909.

Table[Plus@@Transpose[FactorInteger[Cyclotomic[n, 9]]][[2]], {n, 1, 100}]

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

cp's OEIS Frontend

A085034 Number of prime factors of cyclotomic(n,9), which is A019327(n), the value of the n-th cyclotomic polynomial evaluated at x=9.

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