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A326314
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Where the number of divisors d(k) reaches a new record for numbers k whose prime factors are of the form 6*j+5.
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3
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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
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OFFSET
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1,1
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COMMENTS
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For references and links see A326312.
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(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, ", ")))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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