A302935 - OEIS

A302935

Unitary highly composite deficient numbers: unitary deficient numbers k whose number of unitary divisors ud(k) > ud(m) for all unitary deficient numbers m < k.

1, 2, 10, 84, 1155, 25740, 471240, 14549535, 535422888

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

The record numbers of unitary divisors are 1, 2, 4, 8, 16, 32, 64, 128, 256, ...

The unitary version of A302934.

LINKS

Table of n, a(n) for n=1..9.

MATHEMATICA

usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])]; udiv[n_] := 2^PrimeNu[n]; dm = 0; Do[sig = usigma[n]; If[sig >= 2 n, Continue[]]; d = udiv[n]; If[d > dm, Print[n]; dm = d], {n, 1, 1000000000}]

PROG

(PARI) nbud(n) = 1<<omega(n);

usigma(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d));

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

CROSSREFS

Cf. A034444, A034448, A129487, A302934.

Sequence in context: A107863 A065866 A322406 * A332655 A156466 A304403

Adjacent sequences: A302932 A302933 A302934 * A302936 A302937 A302938

KEYWORD

nonn,more

AUTHOR

Amiram Eldar, Apr 16 2018

STATUS

approved