A142337 Numbers n such that sum(i=1..n, sigma(i)) is prime.

7, 12, 18, 23, 24, 32, 49, 66, 84, 87, 90, 92, 111, 112, 113, 114, 129, 130, 132, 133, 137, 138, 199, 238, 239, 271, 275, 278, 283, 285, 307, 313, 314, 317, 319, 322, 340, 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

Offset

1,1

Comments

Numbers n such that A024916(n) is prime.

Links

Table of n, a(n) for n=1..72.

Mathematica

Flatten[Table[If[PrimeQ[Sum[DivisorSigma[1, i], {i, 1, n}]], n, {}], {n, 1, 300}]].
Position[Accumulate[DivisorSigma[1, Range[650]]], _?PrimeQ]//Flatten (* Harvey P. Dale, Oct 12 2020 *)

Prog

(PARI) t=0; for(n=1, 1e3, if(isprime(t+=sigma(n)), print1(n", "))) \\ Charles R Greathouse IV, Nov 07 2011
(Python)
from itertools import count, islice
from math import isqrt
from sympy import isprime
def A142337_gen(startvalue=1): # generator of terms >= startvalue
    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)))
A142337_list = list(islice(A142337_gen(), 30)) # Chai Wah Wu, Oct 23 2023

Crossrefs

Cf. A024916.

Sequence in context: A092094 A064665 A369357 * A131912 A247159 A022953

Adjacent sequences: A142334 A142335 A142336 * A142338 A142339 A142340

Keyword

nonn

Author

Roger L. Bagula and Gary W. Adamson, Sep 18 2008

Extensions

Corrected and extended by Harvey P. Dale, Oct 12 2020

Status

approved