A348936 Numbers k congruent to 1 or 5 mod 6, for which A064989(A064989(sigma(k^2))) > A064989(A064989(k^2)), where A064989 shifts the prime factorization one step towards lower primes, and sigma is the sum of divisors function.

5, 7, 11, 13, 17, 25, 29, 35, 41, 49, 55, 59, 65, 71, 77, 85, 89, 91, 95, 101, 115, 119, 121, 125, 131, 143, 145, 155, 161, 167, 169, 173, 175, 185, 187, 203, 205, 209, 215, 221, 227, 235, 245, 253, 265, 275, 287, 289, 293, 295, 305, 319, 323, 325, 329, 343, 355, 361, 365, 377, 383, 385, 391, 413, 415, 425, 445, 451

Offset

1,1

Comments

Square roots of squares present in A348754.

See comments in A348935.

Links

Table of n, a(n) for n=1..68.

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Mathematica

f[2, e_] := 1; f[p_, e_] := NextPrime[p, -1]^e; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[450], MemberQ[{1, 5}, Mod[#, 6]] && s[s[DivisorSigma[1, #^2]]] > s[s[#^2]] &] (* Amiram Eldar, Nov 04 2021 *)

Prog

(PARI)
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
isA348936(n) = ((n%2)&&(n%3)&&(A064989(A064989(sigma(n^2))) > A064989(A064989(n^2))));

Crossrefs

Cf. A000203, A003961, A007310, A064989, A348750, A348754, A348934, A348935.

Sequence in context: A023201 A106059 A102386 * A346990 A038958 A109416

Adjacent sequences: A348933 A348934 A348935 * A348937 A348938 A348939

Keyword

nonn

Author

Antti Karttunen, Nov 04 2021

Status

approved