A272211 Product of n-th prime and the sum of the divisors of n.

2, 9, 20, 49, 66, 156, 136, 285, 299, 522, 372, 1036, 574, 1032, 1128, 1643, 1062, 2379, 1340, 2982, 2336, 2844, 1992, 5340, 3007, 4242, 4120, 5992, 3270, 8136, 4064, 8253, 6576, 7506, 7152, 13741, 5966, 9780, 9352, 15570, 7518, 17376, 8404, 16212, 15366, 14328, 10128, 27652, 12939, 21297, 16776, 23422

Offset

1,1

Links

Table of n, a(n) for n=1..52.

Formula

a(n) = prime(n)*sigma(n) = A000040(n)*A000203(n).

a(n) = sigma(n*prime(n)) - sigma(n) = A000203(n*A000040(n)) - A000203(n) = A000203(A033286(n)) - A000203(n) = A272173(n) - A000203(n).

Example

For n = 9 the 9th prime is 23, and the sum of the divisors of 9 is 1 + 3 + 9 = 13, and 23*13 = 299, so a(9) = 299.
On the other hand 9*23 = 207 and the sum of the divisors of 207 is 1 + 3 + 9 + 23 + 69 + 207 = 312 and 312 - 13 = 299, so a(9) = 299.

Mathematica

Table[DivisorSigma[1, n]*Prime[n], {n, 1, 50}] (* G. C. Greubel, Apr 27 2016 *)

Prog

(PARI) a(n) = prime(n)*sigma(n); \\ Michel Marcus, Apr 27 2016

Crossrefs

Main diagonal of A272214.

Cf. A000040, A000203, A033286, A272173, A272400.

Sequence in context: A091941 A294540 A248435 * A259035 A093835 A264294

Adjacent sequences: A272208 A272209 A272210 * A272212 A272213 A272214

Keyword

nonn

Author

Omar E. Pol, Apr 26 2016

Status

approved