A050689 Composites whose sum of digits equals number of its prime factors, with multiplicity.

12, 30, 32, 40, 102, 220, 240, 500, 600, 1002, 1012, 1104, 1152, 1210, 1320, 1500, 2001, 2002, 2020, 2040, 2120, 2240, 2300, 3010, 3040, 3300, 4032, 4100, 4320, 5100, 5200, 6400, 7000, 7200, 10001, 10002, 10011, 10030, 10040, 10080, 10140, 10220, 10304, 10800

Offset: 1

Author

Patrick De Geest, Aug 15 1999

Keywords

• nonn
• base

Comments

The sequence is infinite because there are infinitely many primes whose sum of digits is odd (see related comment in A119450). Let p be one of them, and let k be its digital sum. Then p*10^((k-1)/2) is a term. For example, 41*10^2 is a term. - Metin Sariyar, May 30 2020

Examples

			2002 is a term since 2+0+0+2 = 4, and 2002 = 2*7*11*13 has 4 prime factors.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 322 terms from Michael Turniansky)

Crossrefs

Cf. A050690, A057531, A057532, A070274, A070275, A063737, A067077, A119450.

Programs

Mathematica

Select[Range[10300],!PrimeQ[#]&&PrimeOmega[#]==Total[IntegerDigits[#]]&] (* Jayanta Basu, May 30 2013 *)

PARI

isok(n) = sumdigits(n) == bigomega(n); \\ Michel Marcus, Feb 13 2017

Python

from sympy import factorint
def ok(n): return 1 < sum(map(int, str(n))) == sum(factorint(n).values())
print([k for k in range(11000) if ok(k)]) # Michael S. Branicky, Dec 30 2021