A057934 Number of prime factors of 10^n + 1 (counted with multiplicity).

1, 1, 3, 2, 2, 2, 2, 2, 5, 3, 5, 3, 3, 4, 7, 5, 4, 3, 2, 4, 8, 4, 5, 3, 5, 3, 7, 4, 3, 7, 2, 4, 9, 4, 5, 6, 4, 3, 10, 4, 3, 7, 4, 4, 12, 4, 4, 9, 4, 7, 8, 4, 2, 6, 10, 5, 6, 5, 4, 6, 3, 3, 12, 3, 6, 8, 2, 4, 10, 11, 3, 5, 4, 7, 11, 6, 12, 7, 4, 9, 11, 3, 7, 8, 8, 3, 8, 4, 4, 11, 6, 4, 8, 4, 6, 8, 4, 5, 13

Offset

1,3

Comments

2^(a(2n)-1)-1 predicts the number of pair-solutions of even length L for AB = A^2 + B^2. For instance, with length 18 we have 10^18 + 1 = 101*9901*999999000001 or 3 divisors F which when put into the Mersenne formula 2^(F-1)-1 yields 3 pairs (see reference 'Puzzle 104' for details).

Links

Max Alekseyev, Table of n, a(n) for n = 1..331 (first 310 terms from Ray Chandler)

Makoto Kamada, Factorizations of 100...001.

Carlos Rivera, Puzzle 104, The Prime Puzzles & Problems Connection.

S. S. Wagstaff, Jr., Main Tables from the Cunningham Project.

S. S. Wagstaff, Jr., The Cunningham Project

Formula

a(n) = A057951(2n) - A057951(n). - T. D. Noe, Jun 19 2003

Mathematica

PrimeOmega[10^Range[100]+1] (* Harvey P. Dale, May 02 2021 *)

Prog

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

Crossrefs

bigomega(b^n+1): this sequence (b=10), A057935 (b=9), A057936 (b=8), A057937 (b=7), A057938 (b=6), A057939 (b=5), A057940 (b=4), A057941 (b=3), A054992 (b=2).

Cf. A003021, A001271, A046053, A001562, A057951, A119704, A344897.

Sequence in context: A174550 A119704 A104223 * A058758 A122396 A272893

Adjacent sequences: A057931 A057932 A057933 * A057935 A057936 A057937

Keyword

nonn

Author

Patrick De Geest, Oct 15 2000

Status

approved