A095256 Number of numbers not divisible by 10 that stay multiples of themselves when freed of their last n digits.

23, 473, 7053, 93643, 1166714, 13969985, 162725300, 1857511487, 20877697534, 231802823099, 2548286736153, 27785452448917, 300880375389561, 3239062263180829, 34693207724723990, 369957928177109127, 3929837791070240044, 41600963003695964039, 439035480966899467108

Offset: 1

Author

Lekraj Beedassy, Jul 02 2004

Keywords

• base
• nonn

Examples

			We have the following a(1)=23 two-digit numbers not ending in zero: 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 24, 26, 28, 33, 36, 39, 44, 48, 55, 66, 77, 88, 99; each is divisible by its tens digit.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..36
• S. Das Dividing by Dropping Digits

Crossrefs

Cf. A057494.

Programs

Mathematica

k = s = 0; Do[ While[ k < 10^n - 1, k++; s = s + DivisorSigma[ 0, k ]]; Print[s], {n, 9}] (* Robert G. Wilson v, Jun 05 2004 *)

Python

from math import isqrt
def A095256(n): return -(s:=isqrt(m:=10**n))**2+(sum(m//k for k in range(1,s+1))<<1)-(n+1)**2 # Chai Wah Wu, Oct 23 2023

Formula

a(n) = Sum_{r=1..10^n-1} tau(r) = A006218(A002283(n)).

a(n) = A057494(n) - (n+1)^2. - Max Alekseyev, Jan 25 2010

Extensions

a(5)-a(9) from Robert G. Wilson v, Jul 05 2004

a(10) onward from Max Alekseyev, Jan 25 2010, Aug 04 2015