A374604 Denominators of sorted rationals r(n) of the form k/d, where d=(i+1)^m, 1 <= m < bigomega(k), bigomega(k) == 0 (mod i), bigomega(d) == 0 (mod i) and gcd(k, prime(j)) = 1 for all j <= i.

2, 4, 2, 8, 2, 4, 2, 2, 16, 4, 2, 8, 2, 4, 2, 4, 2, 32, 8, 2, 4, 16, 2, 4, 2, 8, 2, 4, 8, 4, 2, 2, 4, 64, 2, 16, 4, 8, 2, 32, 4, 2, 8, 2, 4, 16, 2, 4, 2, 4, 8, 2, 16, 2, 8, 4, 2, 4, 2, 8, 128, 4, 2, 32, 8, 2, 16, 4, 64, 8, 2, 4, 2, 16, 2, 2, 4, 4, 2, 8, 2

Offset

1,1

Comments

r(n) = A374603(n)/a(n).

Links

Friedjof Tellkamp, Table of n, a(n) for n = 1..20000

Example

An example is given in A374603 (numerators corresponding to this sequence).

Mathematica

zmax = 200; fi[id_, z_] := (irat = (id + 2)/(id + 1); ub = z/irat^id; parr = Select[Prime[Range[id + 1, PrimePi[z]]], # <= ub &]; rat = Select[Union[Flatten[Outer[Times, parr, parr]]]/(id + 1), # <= z &];
Do[rat = Select[Union[Flatten[Outer[Times, rat, parr]]], # <= z &], id - 1];
While[ub >= irat^id, ub /= irat; parr = Select[parr, # <= ub &]; rat = Select[Union[rat, Flatten[Outer[Times, rat, parr/(id + 1)]]], # <= z &]];
iw = 1; While[iw <= Length[rat], If[Denominator[rat[[iw]]] >= (id + 1)^2 && (id + 1) rat[[iw]] <= z, AppendTo[rat, (id + 1) rat[[iw]]]]; iw++]; (*append multiples of k/d*)
rat = Select[rat, Mod[PrimeOmega[Numerator[#]], id] == 0 && Mod[PrimeOmega[Denominator[#]], id] == 0 &]; (*remove elements != 0 mod i*)
Return[Union[rat]]; ); getimax[zi_] := (im = 1; While[Prime[im + 1]^(2 im)/(im + 1)^im <= zi, im++]; Return[Max[1, im - 1]]); (*1 for z<625/9, 2 for z<7^6/4^3, ...*)
rrtn = {}; imax = getimax[zmax]; For[i = 1, i <= imax, i++, rrtn = Union[rrtn, fi[i, zmax]]];
Numerator[rrtn] (*A374603*);
a = Denominator[rrtn]

Crossrefs

Cf. A001222, A002410, A374074, A374603 (numerators).

Sequence in context: A073017 A296092 A259111 * A209675 A307669 A171977

Adjacent sequences: A374601 A374602 A374603 * A374605 A374606 A374607

Keyword

nonn,frac

Author

Friedjof Tellkamp, Jul 13 2024

Status

approved