A272173 Product of the sum of the divisors of n and the sum of the divisors of n-th prime.

3, 12, 24, 56, 72, 168, 144, 300, 312, 540, 384, 1064, 588, 1056, 1152, 1674, 1080, 2418, 1360, 3024, 2368, 2880, 2016, 5400, 3038, 4284, 4160, 6048, 3300, 8208, 4096, 8316, 6624, 7560, 7200, 13832, 6004, 9840, 9408, 15660, 7560, 17472, 8448, 16296, 15444, 14400, 10176, 27776

Offset

1,1

Comments

Numbers that occur twice in the sequence include 7560, 816000, 2709504, 31752000. Are there infinitely many? Does any number occur more than twice? - Robert Israel, Sep 12 2018

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = sigma(n)*sigma(prime(n)) = sigma(n)*(1 + prime(n)) = A000203(n)*(1 + A000040(n)) = A000203(n)*A008864(n).

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

a(n) = A000203(n) + A272211(n).

Example

For n = 9 the sum of the divisors of 9 is 1 + 3 + 9 = 13, and the 9th prime is 23, and the sum of the divisors of 23 is 1 + 23 = 24, and 13*24 = 312, so a(9) = 312.
On the other hand 9*23 = 207, and the sum of the divisors of 207 is 1 + 3 + 9 + 23 + 69 + 207 = 312, so a(9) = 312.

Maple

f:= n -> numtheory:-sigma(n)*(1+ithprime(n)):
map(f, [$1..100]); # Robert Israel, Sep 12 2018

Mathematica

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

Prog

(PARI) a(n) = sigma(n)*sigma(prime(n)); \\ Michel Marcus, Apr 27 2016
(Magma) [SumOfDivisors(n)*SumOfDivisors(NthPrime(n)): n in [1..50]]; // Vincenzo Librandi, Sep 13 2018

Crossrefs

Cf. A000040, A000203, A008864, A033286, A272211.

Sequence in context: A112236 A050180 A319422 * A028725 A047166 A076506

Adjacent sequences: A272170 A272171 A272172 * A272174 A272175 A272176

Keyword

nonn

Author

Omar E. Pol, Apr 26 2016

Status

approved