A347379 Möbius transform of A108951, the primorial inflation of n.

1, 1, 5, 2, 29, 5, 209, 4, 30, 29, 2309, 10, 30029, 209, 145, 8, 510509, 30, 9699689, 58, 1045, 2309, 223092869, 20, 870, 30029, 180, 418, 6469693229, 145, 200560490129, 16, 11545, 510509, 6061, 60, 7420738134809, 9699689, 150145, 116, 304250263527209, 1045, 13082761331670029, 4618, 870, 223092869, 614889782588491409

Offset

1,3

Comments

Multiplicative because A108951 is.

Links

Table of n, a(n) for n=1..47.

Index entries for sequences related to primorial numbers.

Formula

a(n) = Sum_{d|n} A008683(n/d) * A108951(d).

a(A000040(n)) = A002110(n) - 1.

From Amiram Eldar, Sep 16 2023: (Start)

Multiplicative with a(p^e) = A034386(p)^e - A034386(p)^(e-1).

Sum_{n>=1} 1/a(n) = Product_{n>=1} (1 + A002110(n)/(A002110(n)-1)^2) = 3.8730356211898760903... . (End)

Mathematica

prim[p_] := Product[Prime[i], {i, 1, PrimePi[p]}]; f[p_, e_] := (pr = prim[p])^e - pr^(e - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 50] (* Amiram Eldar, Sep 16 2023 *)

Prog

(PARI)
A002110(n) = prod(i=1, n, prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A002110(primepi(f[i, 1]))^f[i, 2]) };
A347379(n) = sumdiv(n, d, moebius(n/d)*A108951(d));

Crossrefs

Cf. A000040, A002110, A008683, A034386, A108951.

Sequence in context: A007572 A297812 A360546 * A224494 A095998 A328555

Adjacent sequences: A347376 A347377 A347378 * A347380 A347381 A347382

Keyword

nonn,easy,mult

Author

Antti Karttunen, Sep 01 2021

Status

approved