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A231919
a(n) = 3^n + (4^n - 3^n) * (d(n) - 3), where d(n) = A000005(n).
1
1, 2, -10, 81, -538, 4096, -12010, 65536, 19683, 1048576, -3840010, 49268766, -63920218, 268435456, 1073741824, 8546887871, -16921588858, 205383589230, -272553384010, 3291561314526, 4398046511104, 17592186044416, -70180457820010, 1406245165407356, 847288609443
OFFSET
1,2
COMMENTS
a(n) is negative if and only if n is an odd prime (A065091). If n is prime, then a(n) = - A002250(n). If n is a semiprime (A001358), a(n) gives the n-th power of the number of divisors of n. For example, a(4) = d(4)^4 = 3^4 = 81. Similarly, a(6) = d(6)^6 = 4^6 = 4096.
FORMULA
a(n) = A000244(n) + A005061(n) * (A000005(n) - 3).
MAPLE
with(numtheory); A231919:=n->3^n+(4^n-3^n)*(tau(n)-3); seq(A231919(n), n=1..100);
MATHEMATICA
Table[3^n + (4^n - 3^n)(DivisorSigma[0, n] - 3), {n, 100}]
CROSSREFS
Sequence in context: A063902 A088351 A367432 * A174962 A062396 A218294
KEYWORD
sign,easy,less
AUTHOR
Wesley Ivan Hurt, Nov 15 2013
STATUS
approved