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A351537
Odd numbers k for which sigma(k) is congruent to 2 modulo 4 and is not a multiple of 3.
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
1,1
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
FORMULA
a(n) = A351538(n)/2.
MATHEMATICA
Select[Range[1, 1440, 2], MemberQ[{2, 10}, Mod[DivisorSigma[1, #], 12]] &] (* Michael De Vlieger, Feb 14 2022 *)
PROG
(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
CROSSREFS
Intersection of A191218 and A329963.
Contains A068228 as a subsequence.
Terms of A351538 halved.
Sequence in context: A238675 A140112 A089030 * A351536 A354467 A141122
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 14 2022
STATUS
approved