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A168066 If n = Product p(k)^e(k) then a(n) = (Product (p(k)+1)^e(k) - Product (p(k)-1)^e(k))/2, a(1) = 0.

%I A168066 #12 Jul 08 2023 20:15:49
%S A168066 0,1,1,4,1,5,1,13,6,7,1,17,1,9,8,40,1,22,1,25,10,13,1,53,10,15,28,33,
%T A168066 1,32,1,121,14,19,12,70,1,21,16,79,1,42,1,49,40,25,1,161,14,46,20,57,
%U A168066 1,92,16,105,22,31,1,104,1,33,52,364,18,62,1,73,26,60,1,214,1,39,56,81,18,72
%N A168066 If n = Product p(k)^e(k) then a(n) = (Product (p(k)+1)^e(k) - Product (p(k)-1)^e(k))/2, a(1) = 0.
%C A168066 a(n) = 0 iff n is 1;
%C A168066 a(n) = 1 iff n is a prime;
%C A168066 a(n) = p+q iff n is a biprime, i.e., n = p*q, p <= q primes;
%C A168066 a(n) = (p*q + p*r + q*r)+1 iff n is a triprime, i.e., n = p*q*r, p <= q <= r primes;
%C A168066 a(n) = (p*q*r + p*q*s + p*r*s + q*r*s) + (p+q+r+s) iff n is a quadprime, i.e., n = p*q*r*s, p <= q <= r <= s primes;
%C A168066 ...
%H A168066 Daniel Forgues, <a href="/A168066/b168066.txt">Table of n, a(n) for n = 1..100000</a>
%F A168066 a(n) = (A003959(n) - A003958(n))/2.
%o A168066 (PARI) a(n) = {f = factor(n); return ((prod(k=1, #f~, (f[k, 1]+1)^f[k, 2]) - prod(k=1, #f~, (f[k, 1]-1)^f[k, 2]))/2);} \\ _Michel Marcus_, Jun 13 2013
%Y A168066 Cf. A003958, A003959, A168065.
%K A168066 nonn
%O A168066 1,4
%A A168066 _Daniel Forgues_, Nov 18 2009