A361467 - OEIS

%I #13 May 18 2023 10:40:31

%S 1,12,30,117,56,360,132,1080,775,672,182,3510,306,1584,1680,9801,380,

%T 9300,552,6552,3960,2184,870,32400,2793,3672,19500,15444,992,20160,

%U 1406,88452,5460,4560,7392,90675,1722,6624,9180,60480,1892,47520,2256,21294,43400,10440,2862,294030,16093,33516,11400

%N a(n) = A003961(n) * sigma(A003961(n)), where A003961 is fully multiplicative with a(p) = nextprime(p), and sigma is the sum of divisors function.

%H Winston de Greef, <a href="/A361467/b361467.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>.

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.

%F Multiplicative with a(p^e) = q^e * (q^(e+1) - 1) / (q - 1), where q = nextPrime(p).

%F a(n) = A003961(n) * A003973(n).

%F a(n) = A064987(A003961(n)).

%t f[p_, e_] := (q = NextPrime[p])^e * (q^(e+1) - 1) / (q - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, May 18 2023 *)

%o (PARI)

%o A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961

%o A361467(n) = { my(u=A003961(n)); (u*sigma(u)); };

%Y Cf. A000203, A003961, A003973, A064987, A361468.

%K nonn,mult

%O 1,2

%A _Antti Karttunen_, Mar 20 2023