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

5, 7, 9, 21, 19, 21, 41, 33, 61, 123, 109, 111, 191, 165, 211, 459, 213, 361, 705, 951, 1361, 1319, 3537, 1173, 2195, 2479, 1481, 2111, 3295, 3421, 2313, 5415, 5885, 5891, 11091, 15019, 16371, 35067, 15033, 25061, 33373, 15123, 26057, 31309, 42955, 16691, 48573, 36329, 45845, 62385, 31167, 72201, 62123, 80969, 141399, 151113

Offset: 1

Author

Antti Karttunen, Mar 09 2024

Keywords

• nonn

Comments

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10660
• Index entries for sequences related to primorial numbers

Crossrefs

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

Cf. also A024451, A370129.

Programs

PARI

up_to = 15180;
A002110(n) = prod(i=1,n,prime(i));
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
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); };
v370137 = A370137list(up_to);
A370137(n) = v370137[n];
A370138(n) = A003415(A370137(n));

Formula

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