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A327786
Numbers whose number of distinct prime factors is greater than the sum of their digits.
1
10, 100, 110, 210, 1000, 1001, 1010, 1020, 1100, 1110, 2010, 2100, 10000, 10010, 10020, 10100, 10101, 10110, 10200, 11000, 11010, 11100, 20010, 20020, 20100, 21000, 100000, 100002, 100010, 100011, 100020, 100100, 100110, 100200, 101000, 101010, 101100, 102000
OFFSET
1,1
COMMENTS
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.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 291 terms from Metin Sariyar)
EXAMPLE
For a(4) = 210, 2 + 1 + 0 = 3, 210 = 2*3*5*7 with 4 distinct factors, 4 > 3 so 210 is a term.
MATHEMATICA
Select[Range[10^6], Total[IntegerDigits[#]]<Length[FactorInteger[#]]&]
Select[Range[120000], PrimeNu[#]>Total[IntegerDigits[#]]&] (* Harvey P. Dale, Jul 07 2020 *)
PROG
(PARI) isok(n) = omega(n) > sumdigits(n); \\ Michel Marcus, Sep 25 2019
(Magma) [k:k in [2..110000]| #PrimeDivisors(k) gt &+Intseq(k)]; // Marius A. Burtea, Oct 07 2019
CROSSREFS
Sequence in context: A169662 A124252 A121030 * A154810 A099820 A273245
KEYWORD
nonn,base
AUTHOR
Metin Sariyar, Sep 25 2019
STATUS
approved