This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A163407 #6 Jan 22 2025 12:00:38 %S A163407 0,0,0,4,0,6,0,12,9,10,0,16,0,14,15,24,0,21,0,24,21,22,0,30,25,26,27, %T A163407 32,0,31,0,40,33,34,35,37,0,38,39,42,0,41,0,48,39,46,0,48,49,45,51,56, %U A163407 0,45,55,54,57,58,0,51,0,62,51,60,65,61,0,72,69,59,0,57,0,74,55,80,77,71,0 %N A163407 Sum of semiprime divisors of n with repetition. %C A163407 We regard each prime divisor of n as distinct, and count each product of an unordered, distinct pair of them as a semiprime divisor. %H A163407 Antti Karttunen, <a href="/A163407/b163407.txt">Table of n, a(n) for n = 1..20000</a> %F A163407 If s is the sum of the prime divisors of n with repetition, and ss is the sum of their squares, a(n) = (s^2 - ss) / 2. %e A163407 For n = 12, the prime divisors with repetition are 2,2,3. Distinguishing the 2s as 2 and 2', we have semiprime divisors 2*2', 2*3, and 2'*3, totaling 4+6+6 = 16. %o A163407 (PARI) a(n)=local(fn,p,e,s,ss);fn=factor(n);for(i=1,matsize(fn)[1],p=fn[i,1];e=fn[i,2];s+=p*e;ss+=p^2*e);(s^2-ss)\2 %Y A163407 Cf. A076290, A001358, A001222, A067666. %K A163407 nonn %O A163407 1,4 %A A163407 _Franklin T. Adams-Watters_, Jul 26 2009