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

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

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