OFFSET
1,2
COMMENTS
The record numbers of bi-unitary divisors are 1, 2, 4, 6, 8, 10, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, ...
The bi-unitary version of A302934.
MATHEMATICA
f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bdivnum[n_] := DivisorSum[n, 1 &, Last@Intersection[f@#, f[n/#]] == 1 &]; bsigma[m_] := DivisorSum[m, # &, Last@Intersection[f@#, f[m/#]] == 1 &]; dm = 0; Do[sig = bsigma[n]; If[sig >= 2 n, Continue[]]; d = bdivnum[n]; If[d > dm, Print[n]; dm = d], {n, 1, 1000000000}] (* after Michael De Vlieger at A188999 and A286324 *)
PROG
(PARI) udivs(n) = {my(d = divisors(n)); select(x->(gcd(x, n/x)==1), d); }
gcud(n, m) = vecmax(setintersect(udivs(n), udivs(m)));
biudivs(n) = select(x->(gcud(x, n/x)==1), divisors(n));
lista(nn) = {my(maxd = 0); for(n=1, nn, vbiudiv = biudivs(n); if ((vecsum(vbiudiv) < 2*n) && (#vbiudiv > maxd), print1(n, ", "); maxd = #vbiudiv; ); ); } \\ Michel Marcus, Apr 17 2018
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Apr 16 2018
EXTENSIONS
a(15)-a(17) from Amiram Eldar, Jan 26 2019
STATUS
approved