A379501 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.

2, 16, 216, 422, 470, 51016, 5082, 4446, 864, 106688, 1301846, 880, 204182, 1985872, 236964, 646310, 1030, 176778, 2799756, 96178962, 563400, 62092576, 1566805968, 27274, 559406, -16252236, 1040774592, 263042394, 7794826, 115781204, 13256922, -16386856, -1230440, 376172, -67188814, 222905278, 13547232, 28352541646

Offset: 1

Author

Antti Karttunen, Jan 05 2025

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to binary expansion of n.
• Index entries for sequences related to sigma(n).

Crossrefs

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

Cf. also A378231, A337339.

Programs

PARI

A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A379501(n) = { my(osq=((2*n)-1)^2); ((3/2)*A019565(osq) - A019565(sigma(osq)-osq)); };

Formula

a(n) = A379496(A016754(n)) = A019565(1+A016754(n)) - A379495(A016754(n)).

a(n) = (3/2)*A019565(A016754(n)) - A379495(A016754(n)).