cp's OEIS Frontend

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

%I A351535 #25 Aug 28 2025 10:24:47
%S A351535 5,13,17,29,37,41,53,61,73,89,97,101,109,113,137,149,157,173,181,193,
%T A351535 197,229,233,241,245,257,269,277,281,293,313,317,325,337,349,353,373,
%U A351535 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
%N A351535 Odd numbers k that are not multiples of 3 and for which sigma(k) is congruent to 2 modulo 4.
%C A351535 a(25) = 245 = 5* 7^2 is the first term that is not prime.
%C A351535 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
%H A351535 Bill McEachen, <a href="/A351535/b351535.txt">Table of n, a(n) for n = 1..10000</a>
%H A351535 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%t A351535 Select[Range[1, 700, 2], !Divisible[#, 3] && Mod[DivisorSigma[1, #], 4] == 2 &] (* _Amiram Eldar_, Feb 13 2022 *)
%o A351535 (PARI) isA351535(n) = ((n%2) && (0!=(n%3)) && (2 == (sigma(n)%4)));
%Y A351535 Intersection of A001651 and A191218. Complement of A351533 in A191218.
%Y A351535 Cf. A002144 (subsequence).
%K A351535 nonn,changed
%O A351535 1,1
%A A351535 _Antti Karttunen_, Feb 13 2022