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A224914 Accumulation of products of all divisors of n, positive or negative. 1
-1, 3, 12, -52, -27, 1269, 1318, 5414, 4685, 14685, 14806, 3000790, 3000959, 3039375, 3090000, 2041424, 2041713, 36053937, 36054298, 100054298, 100248779, 100483035, 100483564, 110175797740, 110175782115, 110176239091, 110176770532, 110658660836 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If there is some n > 47 such that a(n) < 0, then there is some k^2 > 47 such that a(k^2) <0.

LINKS

Simon Jensen, Table of n, a(n) for n = 1..10000

S. Jensen, The answer is 47

FORMULA

a(n) = Sum_{i=1..n}(-i)^tau(i) = Sum_{i=1..n} (-i)^A000005(i) = Sum_{i=1..n} A217854(i).

EXAMPLE

a(4) = a(1) + a(2) + a(3) + (-4)^tau(4) = (-1) + 3 + 12 + (-64) = -52

MATHEMATICA

Accumulate@ Table[(-n)^DivisorSigma[0, n], {n, 28}] (* Michael De Vlieger, Mar 18 2016 *)

PROG

(PARI) a(n) = sum(k=1, n, (-k)^numdiv(k)); \\ Michel Marcus, Mar 18 2016

CROSSREFS

Sequence in context: A064036 A195255 A241468 * A227810 A125187 A151190

Adjacent sequences:  A224911 A224912 A224913 * A224915 A224916 A224917

KEYWORD

sign

AUTHOR

Simon Jensen, Apr 19 2013

STATUS

approved

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Last modified October 14 12:45 EDT 2019. Contains 328006 sequences. (Running on oeis4.)