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

1,2

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, ...

Links

Table of n, a(n) for n=1..35.

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

Prog

(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

Crossrefs

Cf. A000005, A002182, A005100.

Sequence in context: A208743 A335853 A247213 * A069050 A343844 A059174

Adjacent sequences: A302931 A302932 A302933 * A302935 A302936 A302937

Keyword

nonn

Author

Amiram Eldar, Apr 16 2018

Status

approved