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Number of divisors of floor(Pi*10^n), Pi=3.14...
3

%I #19 Jul 08 2023 14:32:23

%S 2,2,4,6,8,2,8,8,48,8,16,4,8,8,8,8,72,4,64,96,16,64,128,128,8,24,256,

%T 8,32,64,16,64,192,4,24,40,96,2,32,4,16,48,8,32,16,64,48,8,320,8,32,

%U 48,8,64,192,48,16,32,16,64,96,128,8,120,16,64,32,48,8,32,192,512,64,96,144

%N Number of divisors of floor(Pi*10^n), Pi=3.14...

%H Dario Alejandro Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>.

%H Hisanori Mishima, <a href="https://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/de_pi000.htm">Decimal expansions of pi (n = 0 to 100</a>, <a href="https://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/de_pi100.htm">n = 101 to 200</a>, <a href="https://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/de_pi200.htm">n = 201 to 250)</a>.

%F a(n) = A000005(A011545(n)).

%e For n=4: floor(Pi*10^4)=31415 has divisors: 1,5,61,103,305,515,6283,31415; a(4)=8.

%t Table[ DivisorSigma[ 0, Floor[ Pi*10^n]], {n, 0, 10}] (* _Robert G. Wilson v_, Oct 30 2003 *)

%o (PARI) A089284(n)=numdiv(Pi\.1^n) \\ _M. F. Hasler_, Nov 01 2012

%Y Cf. A089282, A089283, A000796.

%K nonn

%O 0,1

%A _Reinhard Zumkeller_, Oct 30 2003

%E More terms from _Robert G. Wilson v_ and _Ray Chandler_, Oct 30 2003