A115907 Numbers k such that sigma(k) plus the k-th prime is a triangular number.
1, 2, 9, 13, 21, 80, 112, 129, 147, 225, 308, 349, 1063, 1282, 1300, 1635, 1880, 2686, 2956, 3517, 3759, 3907, 4058, 5025, 5196, 6742, 7606, 7708, 9244, 10154, 10596, 11259, 11719, 12687, 13167, 13599, 14081, 14624, 15937, 16437, 16766, 18289
Offset: 1
Keywords
Examples
sigma(1880) + prime(1880) = 20503 = T(202).
Links
- David A. Corneth, Table of n, a(n) for n = 1..11241 (first 1000 from Robert Israel)
Programs
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Maple
filter:= n -> issqr(1+8*(numtheory:-sigma(n)+ithprime(n))): select(filter, [$1..10^5]); # Robert Israel, Nov 07 2018
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Mathematica
Select[Range[25000],IntegerQ[(Sqrt[8(DivisorSigma[1,#]+Prime[#])+ 1]-1)/2]&] (* Harvey P. Dale, Jun 07 2011 *)
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PARI
upto(n) = my(t = 0, res = List(), u = prime(n)); forprime(p = 2, u, t++; c = p + sigma(t); if(ispolygonal(c, 3), listput(res, t))); res \\ David A. Corneth, Nov 08 2018