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

Author

Omar E. Pol, Apr 26 2016

Keywords

• nonn

Examples

			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.
		

Crossrefs

Main diagonal of A272214.

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

Programs

Mathematica

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

PARI

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

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).