A379496 - OEIS

%I #17 Jan 05 2025 22:35:32

%S 2,4,3,4,13,15,5,-16,16,35,33,59,103,189,-3,-188,31,-44,53,-55,123,

%T 225,75,89,216,451,315,385,1153,2037,11,-2284,-171,23,-5,-4160,193,

%U 225,69,-247,271,-1599,453,819,1339,2499,141,-309,422,312,605,65,2143,4239,979,1985,2673,5993,5003,2275,15013,29991,-165

%N a(n) = A019565(1+n) - A019565(A001065(n)), where A019565 is the base-2 exp-function, and A001065 is the sum of proper divisors of n.

%H Antti Karttunen, <a href="/A379496/b379496.txt">Table of n, a(n) for n = 1..32768</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>.

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.

%F a(n) = A019565(1+n) - A379495(n).

%F For even n, a(n) = 2*A019565(n) - A379495(n).

%F For n of the form 4k+1, a(n) = (3/2)*A019565(n) - A379495(n).

%o (PARI)

%o A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };

%o A379496(n) = (A019565(1+n) - A019565(sigma(n)-n));

%Y Cf. A001065, A019565, A379495, A379501 [= a(A016754(n))].

%Y Cf. also A379498.

%K sign

%O 1,1

%A _Antti Karttunen_, Jan 05 2025