A302934 Highly composite deficient numbers: deficient numbers k whose number of divisors d(k) > d(m) for all deficient numbers m < k.

1, 2, 4, 8, 16, 32, 64, 105, 225, 315, 1155, 2475, 4455, 8775, 26325, 27027, 63063, 106029, 247401, 693693, 829521, 969969, 2241603, 3741309, 7894341, 8083075, 32569173, 33671781, 37182145, 56581525, 146791359, 185910725, 622396775, 929553625, 1301375075

Offset: 1

Author

Amiram Eldar, Apr 16 2018

Keywords

• nonn

Comments

The record numbers of divisors are 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 16, 18, 20, 24, 30, 32, 36, 40, 48, 54, 60, 64, 72, 80, 84, 96, 108, 112, 128, 144, 160, 192, 216, 256, 288, ...

Crossrefs

Cf. A000005, A002182, A005100.

Programs

Mathematica

a={}; dm=0; Do[ If[DivisorSigma[1,n]>=2n, Continue[]]; d=DivisorSigma[0,n]; If[d>dm, dm=d; AppendTo[a,n]], {n,1,1000000}]; a

PARI

lista(nn) = {my(maxd = 0); for (n=1, nn, if ((sigma(n) < 2*n) && (numdiv(n) > maxd), maxd = numdiv(n); print1(n, ", ");););} \\ Michel Marcus, Apr 17 2018