A359795 - OEIS

A359795

Dirichlet inverse of function f(n) = 1 + A048675(n), where A048675(n) is fully additive with a(p) = 2^(1-PrimePi(p)).

1, -2, -3, 1, -5, 8, -9, 0, 4, 14, -17, -7, -33, 26, 23, 0, -65, -16, -129, -13, 43, 50, -257, 2, 16, 98, -4, -25, -513, -84, -1025, 0, 83, 194, 77, 24, -2049, 386, 163, 4, -4097, -160, -8193, -49, -52, 770, -16385, 0, 64, -64, 323, -97, -32769, 24, 149, 8, 643, 1538, -65537, 115, -131073, 3074, -100

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Conjecture: the only odd term that occurs more than once is 1 = a(1) = a(4).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..4096

Index entries for sequences computed from indices in prime factorization

FORMULA

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} (1+A048675(n/d)) * a(d).

For n >= 1, a(3^2n) = 4 and a(3^(2n+1)) = -4.

PROG

(PARI)

A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };

memoA359795 = Map();

A359795(n) = if(1==n, 1, my(v); if(mapisdefined(memoA359795, n, &v), v, v = -sumdiv(n, d, if(d<n, (1+A048675(n/d))*A359795(d), 0)); mapput(memoA359795, n, v); (v)));

CROSSREFS

Cf. A000720, A048675, A091428 (positions of odd terms), A359592 (parity of terms).

Cf. also A353348, A359603, A359789, A359790, A359791.

Sequence in context: A242108 A238941 A247582 * A224652 A271497 A293287

Adjacent sequences: A359792 A359793 A359794 * A359796 A359797 A359798

KEYWORD

sign

AUTHOR

Antti Karttunen, Jan 26 2023

STATUS

approved