login
A353793
Multiplicative with a(p^e) = ((q-1)*p)^e, where q is the least prime larger than p.
5
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
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
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, May 11 2022
STATUS
approved