A373969 The smallest number k whose divisors include exactly n Duffinian numbers (A003624).

1, 4, 8, 16, 32, 64, 128, 256, 512, 576, 1152, 1600, 2304, 4608, 3600, 6300, 7200, 18900, 20736, 32725, 14400, 28800, 50400, 56700, 108900, 57600, 100800, 111321, 176400, 129600, 226800, 229075, 360000, 630000, 435600, 333963, 518400, 1374450, 871200, 1001889

Offset

0,2

Comments

Numbers of the form m = 2^(k+1), k >= 0, have exactly k divisors that are Duffinian numbers.

Links

Table of n, a(n) for n=0..39.

Example

Since A003624(1) = 4, a(0) = 1.
The numbers 2 and 3 have no divisors that are Duffinian numbers and 4 = A003624(1), so a(1) = 4.

Mathematica

f[n_] := DivisorSum[n, 1 &, CompositeQ[#] && CoprimeQ[#, DivisorSigma[1, #]] &]; seq[len_, nmax_] := Module[{s = Table[0, {len}], c = 0, n = 1, i}, While[c < len && n < nmax, i = f[n] + 1; If[i <= len && s[[i]] == 0, c++; s[[i]] = n]; n++]; s]; seq[30, 10^7] (* Amiram Eldar, Jul 19 2024 *)

Prog

(Magma) f:=func<n|n ne 1 and not IsPrime(n) and Gcd(n, DivisorSigma(1, n)) eq 1>; a:=[]; for n in [0..38] do k:=1; while #[d:d in Divisors(k)|f(d)] ne n do  k:=k+1; end while; Append(~a, k); end for; a;

Crossrefs

Cf. A003624, A373968.

Sequence in context: A307870 A330873 A233442 * A046055 A186949 A020707

Adjacent sequences: A373966 A373967 A373968 * A373970 A373971 A373972

Keyword

nonn

Author

Marius A. Burtea, Jul 12 2024

Status

approved