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Arithmetic derivatives of the sums of three primorials > 1.
5

%I #7 Mar 09 2024 13:06:09

%S 5,7,9,21,19,21,41,33,61,123,109,111,191,165,211,459,213,361,705,951,

%T 1361,1319,3537,1173,2195,2479,1481,2111,3295,3421,2313,5415,5885,

%U 5891,11091,15019,16371,35067,15033,25061,33373,15123,26057,31309,42955,16691,48573,36329,45845,62385,31167,72201,62123,80969,141399,151113

%N Arithmetic derivatives of the sums of three primorials > 1.

%C For n > 20, a(n) > A369979(n).

%H Antti Karttunen, <a href="/A370138/b370138.txt">Table of n, a(n) for n = 1..10660</a>

%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>

%F a(n) = A003415(A370137(n)).

%o (PARI)

%o up_to = 15180;

%o A002110(n) = prod(i=1,n,prime(i));

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

%o 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 v370137 = A370137list(up_to);

%o A370137(n) = v370137[n];

%o A370138(n) = A003415(A370137(n));

%Y Cf. A000292, A002110, A003415, A369979, A370137.

%Y Cf. also A024451, A370129.

%K nonn

%O 1,1

%A _Antti Karttunen_, Mar 09 2024