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A125131 Product 1-p, where p ranges over the prime factors of n with multiplicity. 2
1, -1, -2, 1, -4, 2, -6, -1, 4, 4, -10, -2, -12, 6, 8, 1, -16, -4, -18, -4, 12, 10, -22, 2, 16, 12, -8, -6, -28, -8, -30, -1, 20, 16, 24, 4, -36, 18, 24, 4, -40, -12, -42, -10, -16, 22, -46, -2, 36, -16, 32, -12, -52, 8, 40, 6, 36, 28, -58, 8, -60, 30, -24, 1, 48, -20, -66, -16, 44, -24, -70, -4, -72, 36, -32 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

f(1), where f is the monic polynomial whose zeros are the prime factors of n with multiplicity.

a(p) = 1-p for any prime number p.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Index to divisibility sequences

FORMULA

Completely multiplicative with a(p) = 1-p. - Franklin T. Adams-Watters, Jan 17 2007

a(n) = f(1), where f(x)=(x-p_1)(x-p_2)...(x-p_m), where { p_1,p_2,...p_m } are the prime factors of n with multiplicity.

a(n) = A003958(n) * A008836(n).

EXAMPLE

a(120) = -8 because the prime factorization of 120 is 2*2*2*3*5, so f(x)=(x-2)(x-2)(x-2)(x-3)(x-5) and f(1)=(-1)*(-1)*(-1)*(-2)*(-4)= -8.

MAPLE

a:= n-> mul((1-i[1])^i[2], i=ifactors(n)[2]):

seq(a(n), n=1..80);  # Alois P. Heinz, Jun 28 2015

MATHEMATICA

f[n_] := Times @@ (-Flatten[Table[ #1, {#2}] & @@@ FactorInteger@n] + 1); Array[g, 80] (* Robert G. Wilson v, Jan 10 2007 *)

PROG

(?) f=polyroot(factor(x)); f(1)

(PARI) a(n)=my(f=factor(n)); prod(i=1, #f~, (1-f[i, 1])^f[i, 2]) \\ Charles R Greathouse IV, Jun 28 2015

CROSSREFS

Cf. A003958, A008836.

Sequence in context: A046791 A187203 A187202 * A003958 A326140 A082729

Adjacent sequences:  A125128 A125129 A125130 * A125132 A125133 A125134

KEYWORD

easy,sign,mult

AUTHOR

Mitch Cervinka (puritan(AT)toast.net), Jan 10 2007

EXTENSIONS

Edited by Franklin T. Adams-Watters, Jan 17 2007

STATUS

approved

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Last modified June 18 07:24 EDT 2019. Contains 324203 sequences. (Running on oeis4.)