A382476 Numbers k where record low values occur for abs(A129132(k)/k - c) = abs(A380264(k)/A380265(k) - c), where c = A033150 is Niven's constant.

1, 2, 3, 4, 8, 9, 16, 18, 20, 24, 25, 27, 28, 32, 56, 64, 81, 128, 162, 176, 192, 256, 352, 384, 736, 768, 896, 1026, 1029, 1056, 1280, 1792, 1863, 1864, 1928, 2052, 2058, 2064, 2080, 2304, 2432, 2560, 2944, 3776, 4376, 4384, 4480, 4482, 5104, 5120, 5121, 5125

Offset

1,2

Comments

First differs from A382475 at n = 72: a(72) = 39937 while A382475(72) = 39936.

Since lim_{k->oo} A129132(k)/k = c, this sequence is infinite if Niven's constant is irrational.

Links

Amiram Eldar, Table of n, a(n) for n = 1..103

Mathematica

f[k_] := Max[FactorInteger[k][[;; , 2]]]; f[1] = 0; seq[lim_] := Module[{Niven = 1 + NSum[1 - 1/Zeta[k], {k, 2, Infinity}, NSumTerms -> 100, WorkingPrecision -> 50], dm = 2, d, s = {}, sum = 0}, Do[sum += f[k]; d = Abs[sum/k - Niven]; If[d < dm, dm = d; AppendTo[s, k]], {k, 1, lim}]; s]; seq[10^4]

Prog

(PARI) default(realprecision, 120);
f(k) = if(k == 1, 0, vecmax(factor(k)[, 2]));
list(lim) = {my(niven = 1 + suminf(k = 2, 1-1/zeta(k)), dm = 2, d, s = List(), sm = 0); for(k = 1, lim, sm += f(k); d = abs(sm/k - niven); if(d < dm, dm = d; listput(s, k))); Vec(s); }

Crossrefs

Cf. A033150, A051903, A129132, A380264, A380265, A382475.

Sequence in context: A373725 A212255 A382475 * A078829 A045583 A045608

Adjacent sequences: A382473 A382474 A382475 * A382477 A382478 A382479

Keyword

nonn

Author

Amiram Eldar, Mar 28 2025

Status

approved