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A081400 a(n) = d(n) - bigomega(n) - A005361(n). 1
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 (list; graph; refs; listen; history; text; internal format)
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: A044934 A124761 A156709 * A131963 A130538 A276007

Adjacent sequences:  A081397 A081398 A081399 * A081401 A081402 A081403

KEYWORD

sign

AUTHOR

Labos Elemer, Mar 28 2003

STATUS

approved

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Last modified October 14 12:02 EDT 2019. Contains 328004 sequences. (Running on oeis4.)