A247884 Number of positive integers < 10^n divisible by their first digit.
9, 41, 327, 3158, 31450, 314349, 3143320, 31433005, 314329833, 3143298089, 31432980631, 314329806030, 3143298060001, 31432980599686, 314329805996514, 3143298059964770, 31432980599647312, 314329805996472711, 3143298059964726682, 31432980599647266367
Offset: 1
Links
- Hiroaki Yamanouchi, Table of n, a(n) for n = 1..100
- Beyond Solutions Blog, Multiple of the first digit
- J. J. O'Connor and E. F. Robertson, Pietro Mengoli
Programs
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PARI
a(n)=c=0;for(k=1,10^n-1,d=digits(k);if(k%d[1]==0,c++));c n=1;while(n<10,print1(a(n),", ");n++)
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Python
count = 9 # Start with the first 9 digits print(1, 9) n = 2 while n < 101: for a in range(1, 10): count += 10**(n-1)//a if 10**(n-1) % a != 0: count += 1 print(n, count) n += 1 # David Consiglio, Jr., Sep 26 2014
Formula
G.f.: x*(9 - 67*x + 24*x^2 + 14*x^3 - 56*x^4 + 21*x^5 + 7*x^6 + 5*x^7)/((1 - x)^2*(1 + x)*(1 - 10*x)*(1 - x + x^2)). - Robert Israel, Mar 10 2025
Extensions
a(9)-a(20) from Hiroaki Yamanouchi, Sep 26 2014
Comments