A050689 - OEIS

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

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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())