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

%I A353793 #15 Dec 31 2022 03:52:19
%S A353793 1,4,12,16,30,48,70,64,144,120,132,192,208,280,360,256,306,576,418,
%T A353793 480,840,528,644,768,900,832,1728,1120,870,1440,1116,1024,1584,1224,
%U A353793 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
%N A353793 Multiplicative with a(p^e) = ((q-1)*p)^e, where q is the least prime larger than p.
%H A353793 Antti Karttunen, <a href="/A353793/b353793.txt">Table of n, a(n) for n = 1..10000</a>
%H A353793 Antti Karttunen, <a href="/A353793/a353793.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A353793 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>.
%F A353793 a(n) = A353791(A003961(n)).
%F A353793 a(n) = n * A339905(n).
%F A353793 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
%t A353793 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 *)
%o A353793 (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); };
%Y A353793 Cf. A003961, A151800, A339905, A353791, A353792, A353794.
%Y A353793 Cf. also A353789.
%K A353793 nonn,mult
%O A353793 1,2
%A A353793 _Antti Karttunen_, May 11 2022