login
A373969
The smallest number k whose divisors include exactly n Duffinian numbers (A003624).
0
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.
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
Sequence in context: A307870 A330873 A233442 * A046055 A186949 A020707
KEYWORD
nonn
AUTHOR
Marius A. Burtea, Jul 12 2024
STATUS
approved