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A194264
Sum of divisors of all elements of the n-th set of consecutive integers that are also nonprimes.
1
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
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
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 03 2011
STATUS
approved