A194264 Sum of divisors of all elements of the n-th set of consecutive integers that are also nonprimes.

1, 7, 12, 46, 28, 79, 39, 110, 229, 72, 304, 206, 96, 234, 444, 482, 168, 555, 366, 195, 642, 433, 764, 1158, 544, 216, 564, 280, 616, 2639, 683, 1210, 288, 2211, 372, 1406, 1389, 834, 1555, 1490, 546, 2788, 508, 1029, 468, 3913, 3948, 1249, 560, 1266, 2006

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Example

46 is in the sequence because the fourth set of consecutive natural numbers that are also nonprimes is {8, 9, 10}, the sum of divisors of 8 is 1+2+4+8=15, the sum of divisors of 9 is 1+3+9=13, the sum of divisors of 10 is 1+2+5+10=18, so a(4) = 15+13+18 = 46.

Maple

with(numtheory):
a:= n-> `if`(n=1, 1, add(sigma(i), i=ithprime(n)+1..ithprime(n+1)-1)):
seq(a(n), n=1..80);  # Alois P. Heinz, Oct 18 2011

Mathematica

Table[Plus@@Flatten[Divisors[Range[Prime[n] - (-1)^Prime[n], Prime[n + 1] + (-1)^Prime[n + 1]]]], {n, 2, 50}] (* Alonso del Arte, Oct 18 2011 *)

Crossrefs

Cf. A000203, A018252, A054265, A055670.

Sequence in context: A113499 A335579 A178681 * A192779 A108238 A038278

Adjacent sequences: A194261 A194262 A194263 * A194265 A194266 A194267

Keyword

nonn,easy

Author

Omar E. Pol, Sep 03 2011

Status

approved