A353793 Multiplicative with a(p^e) = ((q-1)*p)^e, where q is the least prime larger than p.

1, 4, 12, 16, 30, 48, 70, 64, 144, 120, 132, 192, 208, 280, 360, 256, 306, 576, 418, 480, 840, 528, 644, 768, 900, 832, 1728, 1120, 870, 1440, 1116, 1024, 1584, 1224, 2100, 2304, 1480, 1672, 2496, 1920, 1722, 3360, 1978, 2112, 4320, 2576, 2444, 3072, 4900, 3600, 3672, 3328, 3074, 6912, 3960, 4480, 5016, 3480, 3540

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Index entries for sequences computed from indices in prime factorization.

Formula

a(n) = A353791(A003961(n)).

a(n) = n * A339905(n).

Sum_{k=1..n} a(k) ~ c * n^3, where c = (1/3) * Product_{p prime} ((p^2-p)/(p^2-q(p)+1)) = 0.49154782..., where q(p) = nextprime(p) = A151800(p). - Amiram Eldar, Dec 31 2022

Mathematica

f[p_, e_] := ((NextPrime[p] - 1)*p)^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 60] (* Amiram Eldar, Dec 31 2022 *)

Prog

(PARI) A353793(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 1] = f[i, 1]*(nextprime(f[i, 1]+1)-1)); factorback(f); };

Crossrefs

Cf. A003961, A151800, A339905, A353791, A353792, A353794.

Cf. also A353789.

Sequence in context: A152680 A270248 A228274 * A273501 A291781 A348342

Adjacent sequences: A353790 A353791 A353792 * A353794 A353795 A353796

Keyword

nonn,mult

Author

Antti Karttunen, May 11 2022

Status

approved