cp's OEIS Frontend

A370138 Arithmetic derivatives of the sums of three primorials > 1.

%I A370138 #7 Mar 09 2024 13:06:09
%S A370138 5,7,9,21,19,21,41,33,61,123,109,111,191,165,211,459,213,361,705,951,
%T A370138 1361,1319,3537,1173,2195,2479,1481,2111,3295,3421,2313,5415,5885,
%U A370138 5891,11091,15019,16371,35067,15033,25061,33373,15123,26057,31309,42955,16691,48573,36329,45845,62385,31167,72201,62123,80969,141399,151113
%N A370138 Arithmetic derivatives of the sums of three primorials > 1.
%C A370138 For n > 20, a(n) > A369979(n).
%H A370138 Antti Karttunen, <a href="/A370138/b370138.txt">Table of n, a(n) for n = 1..10660</a>
%H A370138 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A370138 a(n) = A003415(A370137(n)).
%o A370138 (PARI)
%o A370138 up_to = 15180;
%o A370138 A002110(n) = prod(i=1,n,prime(i));
%o A370138 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A370138 A370137list(up_to) = { my(v = vector(up_to), i=0); for(x=1,oo, for(y=1,x, for(z=1,y, i++; if(i > up_to, return(v)); v[i] = A002110(x)+A002110(y)+A002110(z)))); (v); };
%o A370138 v370137 = A370137list(up_to);
%o A370138 A370137(n) = v370137[n];
%o A370138 A370138(n) = A003415(A370137(n));
%Y A370138 Cf. A000292, A002110, A003415, A369979, A370137.
%Y A370138 Cf. also A024451, A370129.
%K A370138 nonn
%O A370138 1,1
%A A370138 _Antti Karttunen_, Mar 09 2024