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

1,2

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).

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)).

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 *)

Prog

(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)); };

Crossrefs

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

Sequence in context: A286659 A320483 A361468 * A260417 A117313 A080563

Adjacent sequences: A361464 A361465 A361466 * A361468 A361469 A361470

Keyword

nonn,mult

Author

Antti Karttunen, Mar 20 2023

Status

approved