A326313 Where the number of divisors d(k) reaches a new record for numbers k whose prime factors are of the form 4*j+3.

3, 9, 21, 63, 189, 441, 567, 693, 2079, 4851, 6237, 13167, 39501, 92169, 118503, 276507, 829521, 908523, 2119887, 2725569, 6359661, 19078983, 28164213, 57236949, 84492639, 171710847, 197149491, 591448473, 1211061159, 1774345419, 3633183477, 5323036257, 6505933203

Offset

1,1

Comments

For references and links see A326312.

Links

Amiram Eldar, Table of n, a(n) for n = 1..300

Mathematica

aQ[n_] := AllTrue[FactorInteger[n][[;; , 1]], Mod[#, 4] == 3 &]; s[n_] := DivisorSum[n, 1 &, aQ[#] &]; sm = 0; seq = {}; Do[s1 = s[n]; If[s1 > sm, sm = s1; AppendTo[seq, n]], {n, 2, 10^5}]; seq (* Amiram Eldar, Sep 12 2019 *)

Prog

(PARI) pkn(x, d, m)={my(fn=factor(x), nf=#fn[, 1]); for(k=1, nf, if(fn[k, 1]%d!=m, return(0))); numdiv(x)};
divrecord=0;
for(k=2, 50000000, my(j=pkn(k, 4, 3)); if(j>divrecord, divrecord=j; print1(k, ", ")))

Crossrefs

Cf. A053624, A071383, A230655, A326312, A326314.

Sequence in context: A239663 A004667 A237122 * A073947 A062811 A363693

Adjacent sequences: A326310 A326311 A326312 * A326314 A326315 A326316

Keyword

nonn

Author

Hugo Pfoertner, Sep 11 2019

Extensions

More terms from Amiram Eldar, Sep 12 2019

Status

approved