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A048108 Numbers with at least as many non-unitary divisors (A048105) as unitary divisors (A034444). 6
8, 16, 24, 27, 32, 36, 40, 48, 54, 56, 64, 72, 80, 81, 88, 96, 100, 104, 108, 112, 120, 125, 128, 135, 136, 144, 152, 160, 162, 168, 176, 180, 184, 189, 192, 196, 200, 208, 216, 224, 225, 232, 240, 243, 248, 250, 252, 256, 264, 270, 272, 280, 288, 296, 297 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numbers divisible by a prime cubed or two distinct primes squared. - Charles R Greathouse IV, Jun 07 2013
Equals A013929 \ A060687. The asymptotic density of this sequence is 1 - A059956 - A271971 = 0.1913171761... - Amiram Eldar, Nov 07 2020
LINKS
MAPLE
with(numtheory): for n from 1 to 800 do if 2^nops(ifactors(n)[2])<=tau(n)-2^nops(ifactors(n)[2]) then printf(`%d, `, n) fi; od:
MATHEMATICA
Select[Range[300], Function[n, # <= DivisorSigma[0, n] - # &@ DivisorSum[n, 1 &, CoprimeQ[#, n/#] &]]] (* or *)
Select[Range[300], Or[Count[#, p_ /; Last@ p >= 2] >= 2, Count[#, p_ /; Last@ p >= 3] == 1] &@ FactorInteger@ # &] (* Michael De Vlieger, Aug 01 2017 *)
PROG
(PARI) is(n)=my(f=vecsort(factor(n)[, 2], , 4)); #f && (f[1]>2 || (#f>1 && f[2]>1)) \\ Charles R Greathouse IV, Jun 07 2013
(PARI) is(n)=factorback(factor(n)[, 2]) > 2 \\ Charles R Greathouse IV, Aug 25 2016
CROSSREFS
Complement of A048107.
Subsequence of A013929.
Sequence in context: A122612 A078130 A062171 * A228957 A137845 A046099
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from James A. Sellers, Jun 20 2000
STATUS
approved

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Last modified March 28 13:35 EDT 2024. Contains 371254 sequences. (Running on oeis4.)