A361467 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.

1, 12, 30, 117, 56, 360, 132, 1080, 775, 672, 182, 3510, 306, 1584, 1680, 9801, 380, 9300, 552, 6552, 3960, 2184, 870, 32400, 2793, 3672, 19500, 15444, 992, 20160, 1406, 88452, 5460, 4560, 7392, 90675, 1722, 6624, 9180, 60480, 1892, 47520, 2256, 21294, 43400, 10440, 2862, 294030, 16093, 33516, 11400

Offset: 1

Author

Antti Karttunen, Mar 20 2023

Keywords

• nonn
• mult

Links

• Winston de Greef, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from indices in prime factorization.
• Index entries for sequences related to sigma(n).

Crossrefs

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

Programs

Mathematica

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 *)

PARI

A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A361467(n) = { my(u=A003961(n)); (u*sigma(u)); };

Formula

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

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

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