|
%I #13 Dec 17 2017 03:04:44
%S 1,1,1,3,1,4,1,7,4,8,1,10,1,11,6,15,1,16,1,18,9,19,1,22,6,23,13,25,1,
%T 26,1,31,15,32,8,34,1,35,18,38,1,39,1,41,21,42,1,46,8,47,23,49,1,50,
%U 13,53,27,54,1,56,1,57,30,63,15,64,1,66,32,67,1,70,1,71,35,73,12,74,1,78,40
%N Number of times the smallest prime factor of n is a factor in all numbers <=n; a(1)=1.
%C For n>1, a(n) = 1 iff n is prime.
%C a(n) = A078897(n) iff n is a prime power (A000961).
%H Antti Karttunen, <a href="/A078896/b078896.txt">Table of n, a(n) for n = 1..16384</a>
%t With[{s = Array[Flatten@ Map[ConstantArray[#1, #2] & @@ # &, FactorInteger[#]] &, 81]}, Array[Count[Take[s, #1], #2, 2] & @@ {#, s[[#, 1]]} &, Length@ s]] (* _Michael De Vlieger_, Dec 16 2017 *)
%o (PARI) a(n) = if (n==1, 1, my(p = factor(n)[1, 1]); sum(i=1, n, valuation(i, p))); \\ _Michel Marcus_, Dec 27 2014
%Y Cf. A020639, A078897, A078898.
%K nonn
%O 1,4
%A _Reinhard Zumkeller_, Dec 12 2002
|
