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

1,1

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

Links

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

Example

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

Mathematica

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

Prog

(APL (NARS200 dialect)) ⍸∊{(⍴π⍵)=+/(10⍴10)⊤⍵}¨⍳1E6 ⍝for the numbers through 1000000 Michael Turniansky Feb 13 2017
(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

Crossrefs

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

Sequence in context: A334989 A331367 A335149 * A365041 A144565 A334587

Adjacent sequences: A050686 A050687 A050688 * A050690 A050691 A050692

Keyword

nonn,base

Author

Patrick De Geest, Aug 15 1999

Status

approved