A379501 - OEIS

%I #16 Jan 05 2025 22:38:56

%S 2,16,216,422,470,51016,5082,4446,864,106688,1301846,880,204182,

%T 1985872,236964,646310,1030,176778,2799756,96178962,563400,62092576,

%U 1566805968,27274,559406,-16252236,1040774592,263042394,7794826,115781204,13256922,-16386856,-1230440,376172,-67188814,222905278,13547232,28352541646

%N a(n) = (3/2)*A019565((2n-1)^2) - A019565(A001065((2n-1)^2)), where A019565 is the base-2 exp-function, and A001065 is the sum of proper divisors of n.

%H Antti Karttunen, <a href="/A379501/b379501.txt">Table of n, a(n) for n = 1..16384</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) = A379496(A016754(n)) = A019565(1+A016754(n)) - A379495(A016754(n)).

%F a(n) = (3/2)*A019565(A016754(n)) - A379495(A016754(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 A379501(n) = { my(osq=((2*n)-1)^2); ((3/2)*A019565(osq) - A019565(sigma(osq)-osq)); };

%Y Cf. A001065, A016754, A019565, A379495, A379496.

%Y Cf. also A378231, A337339.

%K sign

%O 1,1

%A _Antti Karttunen_, Jan 05 2025