%I #14 Oct 23 2023 11:38:43
%S 7,12,18,23,24,32,49,66,84,87,90,92,111,112,113,114,129,130,132,133,
%T 137,138,199,238,239,271,275,278,283,285,307,313,314,317,319,322,340,
%U 342,352,357,392,394,397,399,442,443,491,492,494,499,500,505,507,508,541,545,551,552,573,574,589,590,597,598,599,600,610,619,622,648,649,650
%N Numbers n such that sum(i=1..n, sigma(i)) is prime.
%C Numbers n such that A024916(n) is prime.
%t Flatten[Table[If[PrimeQ[Sum[DivisorSigma[1, i], {i, 1, n}]], n, {}], {n, 1, 300}]].
%t Position[Accumulate[DivisorSigma[1,Range[650]]],_?PrimeQ]//Flatten (* _Harvey P. Dale_, Oct 12 2020 *)
%o (PARI) t=0;for(n=1,1e3,if(isprime(t+=sigma(n)),print1(n", "))) \\ _Charles R Greathouse IV_, Nov 07 2011
%o (Python)
%o from itertools import count, islice
%o from math import isqrt
%o from sympy import isprime
%o def A142337_gen(startvalue=1): # generator of terms >= startvalue
%o return filter(lambda n: isprime(-(s:=isqrt(n))**2*(s+1) + sum((q:=n//k)*((k<<1)+q+1) for k in range(1,s+1))>>1), count(max(startvalue,1)))
%o A142337_list = list(islice(A142337_gen(),30)) # _Chai Wah Wu_, Oct 23 2023
%Y Cf. A024916.
%K nonn
%O 1,1
%A _Roger L. Bagula_ and _Gary W. Adamson_, Sep 18 2008
%E Corrected and extended by _Harvey P. Dale_, Oct 12 2020