

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
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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[#]]&]


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

Cf. A001221, A165256.
Sequence in context: A169662 A124252 A121030 * A154810 A099820 A273245
Adjacent sequences: A327783 A327784 A327785 * A327787 A327788 A327789


KEYWORD

nonn,base


AUTHOR

Metin Sariyar, Sep 25 2019


STATUS

approved



