A351952 - OEIS

%I #14 Oct 23 2024 10:50:47

%S 0,1,1,5,2,7,1,7,8,31,13,41,2,9,11,37,16,47,3,11,14,43,19,53,1,9,10,

%T 41,17,55,12,59,71,247,106,317,19,73,92,289,127,359,26,87,113,331,148,

%U 401,2,11,13,47,20,61,17,69,86,277,121,347,24,83,107,319,142,389,31,97,128,361,163,431,3,13,16,53,23,67

%N a(n) = A351950(n) / A351577(n).

%C Compare how different the scatter plot is to that of A342002, albeit with a very similar definition.

%C Note: this is at least partly because the other uses linear and the other uses logarithmic scatter plot. - _Antti Karttunen_, Oct 23 2024

%H Antti Karttunen, <a href="/A351952/b351952.txt">Table of n, a(n) for n = 0..20160</a>

%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>

%F a(n) = A351950(n) / A351577(n).

%F a(n) = A342001(A276076(n)) = A083345(A276076(n)).

%F a(n) = A342002(A351576(n)).

%F a(n) = A351953(A225901(n)).

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A003557(n) = (n/factorback(factorint(n)[, 1]));

%o A276076(n) = { my(i=0,m=1,f=1,nextf); while((n>0),i=i+1; nextf = (i+1)*f; if((n%nextf),m*=(prime(i)^((n%nextf)/f));n-=(n%nextf));f=nextf); m; };

%o A351952(n) = { my(u=A276076(n)); (A003415(u) / A003557(u)); };

%Y Cf. A000142 (positions of 1's), A003415, A003557, A083345, A225901, A276076, A342001, A342002, A351576, A351577, A351950, A351953, A351954.

%K nonn,base,look

%O 0,4

%A _Antti Karttunen_, Apr 01 2022