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

Author

Omar E. Pol, Sep 03 2011

Keywords

• nonn
• easy

Examples

			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.
		

Links

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

Crossrefs

Cf. A000203, A018252, A054265, A055670.

Programs

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 *)