A326314 Where the number of divisors d(k) reaches a new record for numbers k whose prime factors are of the form 6*j+5.

5, 25, 55, 275, 935, 3025, 4675, 21505, 51425, 107525, 537625, 1182775, 2688125, 3118225, 15591125, 34300475, 77955625, 127847225, 583108075, 639236125, 1406319475, 3196180625, 6008819575, 23907431075, 30044097875, 66097015325, 150220489375, 318467437475, 1123649260525

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[#, 6] == 5 &]; 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, 200000000, my(j=pkn(k, 6, 5)); if(j>divrecord, divrecord=j; print1(k, ", ")))

Crossrefs

Cf. A053624, A071383, A230655, A326312, A326313.

Sequence in context: A161143 A045576 A146649 * A273357 A146412 A228169

Adjacent sequences: A326311 A326312 A326313 * A326315 A326316 A326317

Keyword

nonn

Author

Hugo Pfoertner, Sep 11 2019

Extensions

More terms from Amiram Eldar, Sep 12 2019

Status

approved