A141114 -id:A141114

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A141113

Positive integers k such that d(d(k)) divides k, where d(k) is the number of divisors of k.

+10
4

1, 2, 4, 6, 12, 15, 16, 20, 21, 24, 27, 28, 32, 33, 36, 39, 40, 44, 48, 51, 52, 56, 57, 60, 64, 68, 69, 72, 76, 80, 84, 87, 88, 90, 92, 93, 96, 104, 108, 111, 112, 116, 120, 123, 124, 126, 128, 129, 132, 136, 141, 144, 148, 150, 152, 156, 159, 164, 172, 176, 177, 180

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

OFFSET

1,2

LINKS

Jinyuan Wang, Table of n, a(n) for n = 1..10000

EXAMPLE

28 has 6 divisors and 6 has 4 divisors. 4 divides 28, so 28 is in the sequence.

MAPLE

with(numtheory): a:=proc(n) if `mod`(n, tau(tau(n))) = 0 then n else end if end proc: seq(a(n), n=1..200); # Emeric Deutsch, Jun 05 2008

MATHEMATICA

Select[Range[200], Divisible[#, DivisorSigma[0, DivisorSigma[0, #]]]&] (* Harvey P. Dale, Feb 05 2012 *)

PROG

(PARI) is(k) = k%numdiv(numdiv(k)) == 0; \\ Jinyuan Wang, Feb 19 2019

CROSSREFS

Cf. A000005 (tau), A010553, A141114, A141115.

KEYWORD

nonn

AUTHOR

Leroy Quet, Jun 04 2008

EXTENSIONS

More terms from Emeric Deutsch, Jun 05 2008

STATUS

approved

A141115

Those positive integers k where both d(d(k)) is not coprime to k and d(d(k)) does not divide k, where d(k) is the number of divisors of k.

+10
3

18, 30, 42, 50, 54, 66, 70, 78, 98, 102, 110, 114, 130, 138, 140, 154, 160, 162, 170, 174, 182, 186, 190, 200, 220, 222, 224, 230, 238, 242, 246, 250, 258, 260, 266, 282, 286, 290, 308, 310, 315, 318, 322, 338, 340, 350, 352, 354, 364, 366, 370, 374, 380, 392