A302936 Bi-unitary highly composite deficient numbers: bi-unitary deficient numbers k whose number of bi-unitary divisors bd(k) > bd(m) for all bi-unitary deficient numbers m < k.

1, 2, 8, 32, 84, 512, 972, 1155, 13365, 25740, 318087, 612612, 11223927, 14549535, 440374077, 746503065, 19013596875

Offset: 1

Author

Amiram Eldar, Apr 16 2018

Keywords

• nonn
• more

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.

Crossrefs

Cf. A188999, A286324, A292982, A293185, A302934.

Programs

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 *)

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

Extensions

a(15)-a(17) from Amiram Eldar, Jan 26 2019