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A272211
Product of n-th prime and the sum of the divisors of n.
3
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
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.
Sequence in context: A091941 A294540 A248435 * A259035 A093835 A264294
KEYWORD
nonn
AUTHOR
Omar E. Pol, Apr 26 2016
STATUS
approved