A127413 -id:A127413 - cp's OEIS frontend

A308260 a(n) = Product_{k=1..n, gcd(n,k) = 1} prime(k).

1, 2, 2, 6, 10, 210, 22, 30030, 1870, 149226, 3910, 6469693230, 11594, 7420738134810, 3215630, 741422598, 2569288370, 32589158477190044730, 28045886, 117288381359406970983270, 19644868330, 4812825965463978, 23916676633630, 3217644767340672907899084554130

Offset: 0

Ilya Gutkovskiy, May 30 2019

nonn

Cf. A000010, A000040, A001221, A001783, A002110, A005117, A006093, A127413.

a[n_] := Product[If[GCD[n, k] == 1, Prime[k], 1], {k, 1, n}]; Table[a[n], {n, 0, 23}]

A001221(a(n)) = A000010(n).

a(A000040(n)) = A002110(A006093(n)).

A357210 a(n) = Sum_{k=1..n} prime(k/gcd(n,k)).

Original entry on oeis.org

2, 4, 7, 11, 19, 22, 43, 46, 66, 68, 131, 90, 199, 158, 187, 223, 383, 242, 503, 320, 441, 478, 793, 436, 824, 716, 879, 734, 1373, 658, 1595, 1118, 1313, 1358, 1579, 1103, 2429, 1776, 1957, 1556, 3089, 1532, 3449, 2192, 2347, 2784, 4229, 2144, 4134, 2882, 3687, 3258, 5591

Offset: 1

Ilya Gutkovskiy, Sep 19 2022

nonn

Inverse Moebius transform of A127413.

Cf. A000040, A057661, A127413, A130029, A333558.

Table[Sum[Prime[k/GCD[n, k]], {k, 1, n}], {n, 1, 53}]

a(n) = sum(k=1, n, prime(k/gcd(n,k))); \\ Michel Marcus, Sep 20 2022

a(n) = Sum_{d|n} A127413(d).

cp's OEIS Frontend

A308260 a(n) = Product_{k=1..n, gcd(n,k) = 1} prime(k).

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