A081400 a(n) = d(n) - bigomega(n) - A005361(n).

0, 0, 0, -1, 0, 1, 0, -2, -1, 1, 0, 1, 0, 1, 1, -3, 0, 1, 0, 1, 1, 1, 0, 1, -1, 1, -2, 1, 0, 4, 0, -4, 1, 1, 1, 1, 0, 1, 1, 1, 0, 4, 0, 1, 1, 1, 0, 1, -1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 6, 0, 1, 1, -5, 1, 4, 0, 1, 1, 4, 0, 1, 0, 1, 1, 1, 1, 4, 0, 1, -3, 1, 0, 6, 1, 1, 1, 1, 0, 6, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 4, 0, 1, 4, 1, 0, 1, 0, 4, 1, 1, 0, 4, 1, 1, 1, 1, 1, 8, -1, 1

Offset

1,8

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000005(n) - A001222(n) - A005361(n).

Example

Negative for true prime powers; zero for 1 and primes; see also A030231, A007304, A034683, A075819 etc. to judge about positivity or magnitude.

Prog

(PARI) a(n) = my(f=factor(n)); numdiv(n) - bigomega(n) - prod(k=1, #f~, f[k, 2]); \\ Michel Marcus, May 25 2017
(Python)
from sympy import primefactors, factorint, divisor_count
from operator import mul
def bigomega(n): return 0 if n==1 else bigomega(n/primefactors(n)[0]) + 1
def a005361(n):
    f=factorint(n)
    return 1 if n==1 else reduce(mul, [f[i] for i in f])
def a(n): return divisor_count(n) - bigomega(n) - a005361(n) # Indranil Ghosh, May 25 2017

Crossrefs

Cf. A000005, A001222, A005361, A030231, A030230, A007304, A034683, A075819.

Sequence in context: A333925 A342595 A156709 * A328194 A131963 A130538

Adjacent sequences: A081397 A081398 A081399 * A081401 A081402 A081403

Keyword

sign

Author

Labos Elemer, Mar 28 2003

Status

approved