cp's OEIS Frontend

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

%I A050689 #38 Dec 30 2021 10:49:48
%S A050689 12,30,32,40,102,220,240,500,600,1002,1012,1104,1152,1210,1320,1500,
%T A050689 2001,2002,2020,2040,2120,2240,2300,3010,3040,3300,4032,4100,4320,
%U A050689 5100,5200,6400,7000,7200,10001,10002,10011,10030,10040,10080,10140,10220,10304,10800
%N A050689 Composites whose sum of digits equals number of its prime factors, with multiplicity.
%C A050689 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
%H A050689 Giovanni Resta, <a href="/A050689/b050689.txt">Table of n, a(n) for n = 1..10000</a> (first 322 terms from Michael Turniansky)
%e A050689 2002 is a term since 2+0+0+2 = 4, and 2002 = 2*7*11*13 has 4 prime factors.
%t A050689 Select[Range[10300],!PrimeQ[#]&&PrimeOmega[#]==Total[IntegerDigits[#]]&] (* _Jayanta Basu_, May 30 2013 *)
%o A050689 (APL (NARS200 dialect)) ⍸∊{(⍴π⍵)=+/(10⍴10)⊤⍵}¨⍳1E6 ⍝for the numbers through 1000000 _Michael Turniansky_ Feb 13 2017
%o A050689 (PARI) isok(n) = sumdigits(n) == bigomega(n); \\ _Michel Marcus_, Feb 13 2017
%o A050689 (Python)
%o A050689 from sympy import factorint
%o A050689 def ok(n): return 1 < sum(map(int, str(n))) == sum(factorint(n).values())
%o A050689 print([k for k in range(11000) if ok(k)]) # _Michael S. Branicky_, Dec 30 2021
%Y A050689 Cf. A050690, A057531, A057532, A070274, A070275, A063737, A067077, A119450.
%K A050689 nonn,base
%O A050689 1,1
%A A050689 _Patrick De Geest_, Aug 15 1999