A130029 a(n) = Sum_{d|n} phi(n/d) * prime(d).

2, 5, 9, 14, 19, 28, 29, 40, 45, 60, 51, 88, 65, 90, 105, 114, 91, 150, 103, 178, 161, 160, 127, 252, 181, 202, 215, 268, 165, 352, 187, 306, 289, 278, 331, 462, 229, 320, 357, 506, 259, 542, 275, 474, 537, 392, 303, 706, 413, 586, 495, 590, 345, 720, 571, 764, 565, 520

Offset

1,1

Comments

Old name: A054523 * A000040.

Links

Table of n, a(n) for n=1..58.

Formula

A054523 as an infinite lower triangular matrix * A000040 (the primes) as a vector.

a(n) = Sum_{k=1..n} prime(gcd(n,k)). - Ilya Gutkovskiy, Mar 22 2020

Example

a(4) = 14 = dot product of row 4 of A054523, (2, 1, 0, 1) and primes (2, 3, 5, 7) = (4 + 3 + 0 + 7) = 14.

Maple

A130029 := proc(n)
add( A054523(n, k)*ithprime(k), k=1..n) ;
end proc: # R. J. Mathar, Apr 04 2012

Prog

(PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*prime(d)); \\ Michel Marcus, Mar 22 2020

Crossrefs

Cf. A000010, A000040, A054523, A129691, A130030.

Sequence in context: A160663 A024201 A110443 * A266450 A361742 A132296

Adjacent sequences: A130026 A130027 A130028 * A130030 A130031 A130032

Keyword

nonn

Author

Gary W. Adamson, May 02 2007

Extensions

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

Status

approved