A374127 - OEIS

%I #8 Jul 06 2024 11:06:19

%S 0,-1,-2,-1,-4,1,-6,1,-2,1,-10,9,-12,1,1,7,-16,13,-18,13,1,1,-22,27,

%T -4,1,4,17,-28,32,-30,21,1,1,1,45,-36,1,1,39,-40,42,-42,25,22,1,-46,

%U 65,-6,31,1,29,-52,55,1,51,1,1,-58,96,-60,1,28,51,1,62,-66,37,1,60,-70,111,-72,1,36,41,1,72,-78,93,28

%N a(n) = (sigma(n) - sopfr(n)) - n, where sigma is the sum of divisors, and sopfr is the sum of prime factors (with repetition).

%H Antti Karttunen, <a href="/A374127/b374127.txt">Table of n, a(n) for n = 1..16384</a>

%F a(n) = A086665(n) - n.

%F a(n) = A000203(n) - A075254(n);

%o (PARI)

%o A001414(n) = ((n=factor(n))[, 1]~*n[, 2]);

%o A374127(n) = ((sigma(n)-A001414(n))-n);

%Y Cf. A000203, A001414, A075254, A086665, A374128, A374129.

%K sign

%O 1,3

%A _Antti Karttunen_, Jul 06 2024