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

13, 37, 61, 73, 97, 109, 117, 157, 181, 193, 229, 241, 277, 313, 325, 333, 337, 349, 373, 397, 409, 421, 433, 457, 541, 549, 577, 601, 613, 657, 661, 673, 709, 733, 757, 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

Offset: 1

Author

Antti Karttunen, Feb 14 2022

Keywords

• nonn

Comments

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

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A191218 and A329963.

Contains A068228 as a subsequence.

Terms of A351538 halved.

Programs

Mathematica

Select[Range[1, 1440, 2], MemberQ[{2, 10}, Mod[DivisorSigma[1, #], 12]] &] (* Michael De Vlieger, Feb 14 2022 *)

PARI

isA351537(n) = if(!(n%2),0,my(s=sigma(n)); (2 == (s%4)) && (0 != (s%3)));

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

Formula

a(n) = A351538(n)/2.