cp's OEIS Frontend

A351537 Odd numbers k for which sigma(k) is congruent to 2 modulo 4 and is not a multiple of 3.

%I A351537 #17 Feb 16 2022 23:03:42
%S A351537 13,37,61,73,97,109,117,157,181,193,229,241,277,313,325,333,337,349,
%T A351537 373,397,409,421,433,457,541,549,577,601,613,657,661,673,709,733,757,
%U A351537 769,829,853,873,877,925,937,981,997,1009,1021,1033,1053,1069,1093,1117,1129,1153,1201,1213,1237,1249,1297,1321,1381,1413
%N A351537 Odd numbers k for which sigma(k) is congruent to 2 modulo 4 and is not a multiple of 3.
%C A351537 Terms are of the form p^e*m^2 where e is 1 or 9 mod 12, p is a prime = 1 mod 12 and m is an odd number not divisible by p with sigma(m^2) not divisible by 3, i.e., q^e || m implies e is not 1 mod 3 or q = 2 mod 3. - _Charles R Greathouse IV_, Feb 14 2022
%H A351537 Charles R Greathouse IV, <a href="/A351537/b351537.txt">Table of n, a(n) for n = 1..10000</a>
%F A351537 a(n) = A351538(n)/2.
%t A351537 Select[Range[1, 1440, 2], MemberQ[{2, 10}, Mod[DivisorSigma[1, #], 12]] &] (* _Michael De Vlieger_, Feb 14 2022 *)
%o A351537 (PARI) isA351537(n) = if(!(n%2),0,my(s=sigma(n)); (2 == (s%4)) && (0 != (s%3)));
%o A351537 (PARI) list(lim)=my(v=List()); forstep(m=1,sqrtint(lim\13),2, my(m2=m^2); if(sigma(m2)%3==0,next); forprimestep(p=13,lim\m2,12, m%p && listput(v,p*m2))); forstep(e=9,logint(lim\1,13),[4,8], forstep(m=1,sqrtint(lim\13^e),2, my(m2=m^2); if(sigma(m2)%3==0,next); forprimestep(p=13,lim\m2,12, m%p && listput(v,p^e*m2)))); Set(v) \\ _Charles R Greathouse IV_, Feb 14 2022
%Y A351537 Intersection of A191218 and A329963.
%Y A351537 Contains A068228 as a subsequence.
%Y A351537 Terms of A351538 halved.
%K A351537 nonn
%O A351537 1,1
%A A351537 _Antti Karttunen_, Feb 14 2022