A351535 Odd numbers k that are not multiples of 3 and for which sigma(k) is congruent to 2 modulo 4.

5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149, 157, 173, 181, 193, 197, 229, 233, 241, 245, 257, 269, 277, 281, 293, 313, 317, 325, 337, 349, 353, 373, 389, 397, 401, 409, 421, 425, 433, 449, 457, 461, 509, 521, 541, 557, 569, 577, 593, 601, 605, 613, 617, 637, 641, 653, 661, 673, 677, 701, 709

Offset: 1

Author

Antti Karttunen, Feb 13 2022

Keywords

• nonn
• changed

Comments

a(25) = 245 = 5* 7^2 is the first term that is not prime.

The sequence shows a steady high percentage of primes. The percentages of the number of prime terms in the first 10^3, ..., 10^8 terms are 86.9, 86.6, 87.1, 87.8, 88.4, 88.8. Additionally, approx 99% of the composite terms indivisible by 5 belong to A348938. - Bill McEachen, Aug 21 2025

Links

• Bill McEachen, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to sigma(n)

Crossrefs

Intersection of A001651 and A191218. Complement of A351533 in A191218.

Cf. A002144 (subsequence).

Programs

Mathematica

Select[Range[1, 700, 2], !Divisible[#, 3] && Mod[DivisorSigma[1, #], 4] == 2 &] (* Amiram Eldar, Feb 13 2022 *)

PARI

isA351535(n) = ((n%2) && (0!=(n%3)) && (2 == (sigma(n)%4)));