A348933 Numbers k congruent to 1 or 5 mod 6, for which A348930(k^2) < k^2.

7, 13, 19, 31, 35, 37, 43, 61, 65, 67, 73, 77, 79, 91, 95, 97, 103, 109, 119, 127, 133, 139, 143, 151, 155, 157, 161, 163, 175, 181, 185, 193, 199, 203, 209, 211, 215, 217, 221, 223, 229, 241, 247, 259, 271, 277, 283, 287, 299, 301, 305, 307, 313, 323, 325, 329, 331, 335, 337, 341, 349, 365, 367, 371, 373, 377, 379

Offset

1,1

Comments

Any hypothetical odd term y of A005820 must by necessity be a square. If y is also a nonmultiple of 3, then the square root x = A000196(y) of such a number y must satisfy the condition that for all nontrivial unitary divisor pairs d and x/d [with gcd(d,x/d) = 1, 1 < d < x], the other divisor should reside in this sequence, and the other divisor in A348934. The explanation is similar to the one given in A348738. See also comments in A348935.

Links

Table of n, a(n) for n=1..67.

Index entries for sequences related to sigma(n)

Mathematica

s[n_] := n / 3^IntegerExponent[n, 3]; Select[Range[400], MemberQ[{1, 5}, Mod[#, 6]] && s[DivisorSigma[1, #^2]] < #^2 &] (* Amiram Eldar, Nov 04 2021 *)

Prog

(PARI)
A038502(n) = (n/3^valuation(n, 3));
A348930(n) = A038502(sigma(n));
isA348933(n) = ((n%2)&&(n%3)&&(A348930(n^2)<(n^2)));

Crossrefs

Cf. A000196, A005820, A348738, A348930, A348931, A348934, A348935.

Sequence in context: A287217 A101324 A216830 * A167462 A357277 A088513

Adjacent sequences: A348930 A348931 A348932 * A348934 A348935 A348936

Keyword

nonn

Author

Antti Karttunen, Nov 04 2021

Status

approved