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

Author

Antti Karttunen, May 11 2022

Keywords

• nonn
• mult

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.

Crossrefs

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

Cf. also A353789.

Programs

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 *)

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); };

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