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 A348933 Numbers k congruent to 1 or 5 mod 6, for which A348930(k^2) < k^2. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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 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 A088513 A004611 Adjacent sequences:  A348930 A348931 A348932 * A348934 A348935 A348936 KEYWORD nonn AUTHOR Antti Karttunen, Nov 04 2021 STATUS approved

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Last modified May 27 02:41 EDT 2022. Contains 354093 sequences. (Running on oeis4.)