A130030 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A130030

a(n) = Sum_{d|n} (-1)^omega(n/d) * phi(rad(n/d)) * prime(d).

1

2, 1, 1, 2, 3, 6, 5, 7, 9, 14, 11, 15, 17, 20, 21, 22, 27, 20, 31, 23, 33, 38, 39, 20, 45, 48, 43, 35, 53, 6, 67, 47, 65, 64, 63, 25, 85, 78, 73, 34, 99, 20, 107, 63, 45, 94, 119, 35, 113, 56, 99, 73, 137, 54, 103, 54, 117, 134, 161, -1, 163, 136, 73, 96, 113, 24, 199, 107, 159, 12, 213

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

OFFSET

1,1

COMMENTS

Old name: A129691 * A000040.

A130029 = A054523 * A000040.

LINKS

Table of n, a(n) for n=1..71.

FORMULA

A129691 as an infinite lower triangular matrix * A000040, the primes.

From Ilya Gutkovskiy, Mar 22 2020: (Start)

a(n) = Sum_{d|n} A023900(n/d) * prime(d).

Sum_{k=1..n} a(gcd(n,k)) = prime(n). (End)

EXAMPLE

a(4) = 2 = dot product of row 4 of A129691: (-1, -1, 0, 1) and the first four primes: (2, 3, 5, 7) = (-2, -3, 0, 7) = 2.

CROSSREFS

Cf. A000010, A000040, A001221, A007444, A007947, A023900, A054523, A076479, A129691, A130029, A333177.

Sequence in context: A191631 A025259 A212359 * A088022 A284999 A016732

Adjacent sequences: A130027 A130028 A130029 * A130031 A130032 A130033

KEYWORD

sign

AUTHOR

Gary W. Adamson, May 02 2007

EXTENSIONS

New name and more terms from Ilya Gutkovskiy, Mar 22 2020

STATUS

approved