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A327786 Numbers whose number of distinct prime factors is greater than the sum of their digits. 1

%I #28 Sep 08 2022 08:46:24

%S 10,100,110,210,1000,1001,1010,1020,1100,1110,2010,2100,10000,10010,

%T 10020,10100,10101,10110,10200,11000,11010,11100,20010,20020,20100,

%U 21000,100000,100002,100010,100011,100020,100100,100110,100200,101000,101010,101100,102000

%N Numbers whose number of distinct prime factors is greater than the sum of their digits.

%C The sequence is infinite since every number of the form 10^k for k >= 1 is in the sequence. It can be proved that 210 is the largest term with distinct digits.

%H Giovanni Resta, <a href="/A327786/b327786.txt">Table of n, a(n) for n = 1..10000</a> (first 291 terms from Metin Sariyar)

%e For a(4) = 210, 2 + 1 + 0 = 3, 210 = 2*3*5*7 with 4 distinct factors, 4 > 3 so 210 is a term.

%t Select[Range[10^6], Total[IntegerDigits[#]]<Length[FactorInteger[#]]&]

%t Select[Range[120000],PrimeNu[#]>Total[IntegerDigits[#]]&] (* _Harvey P. Dale_, Jul 07 2020 *)

%o (PARI) isok(n) = omega(n) > sumdigits(n); \\ _Michel Marcus_, Sep 25 2019

%o (Magma) [k:k in [2..110000]| #PrimeDivisors(k) gt &+Intseq(k)]; // _Marius A. Burtea_, Oct 07 2019

%Y Cf. A001221, A165256.

%K nonn,base

%O 1,1

%A _Metin Sariyar_, Sep 25 2019

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)