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

Author

Metin Sariyar, Sep 25 2019

Keywords

• nonn
• base

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.

Examples

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

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 291 terms from Metin Sariyar)

Crossrefs

Cf. A001221, A165256.

Programs

Magma

[k:k in [2..110000]| #PrimeDivisors(k) gt &+Intseq(k)]; // Marius A. Burtea, Oct 07 2019

Mathematica

Select[Range[10^6], Total[IntegerDigits[#]]Total[IntegerDigits[#]]&] (* Harvey P. Dale, Jul 07 2020 *)

PARI

isok(n) = omega(n) > sumdigits(n); \\ Michel Marcus, Sep 25 2019