cp's OEIS Frontend

A280971 Composite numbers having the same bits as their prime factors (with multiplicity), including zero bits.

%I A280971 #12 Apr 21 2025 02:35:20
%S A280971 159,287,303,319,591,623,679,687,699,763,1135,1167,1203,1243,1247,
%T A280971 1271,1351,1371,1391,1631,2167,2173,2231,2285,2319,2359,2463,2471,
%U A280971 2495,2519,2743,2779,2787,2809,2863,2931,2933,2991,3029,3039,3503,4223,4279,4287,4319,4343,4411,4439,4479,4487
%N A280971 Composite numbers having the same bits as their prime factors (with multiplicity), including zero bits.
%C A280971 Binary equivalent of A280928.
%C A280971 Subsequence of A278909 as well as A280967. The terms in A278909 and A280967 but not this sequence are given by A280972.
%H A280971 Ely Golden, <a href="/A280971/b280971.txt">Table of n, a(n) for n = 1..10000</a>
%o A280971 (SageMath)
%o A280971 def factorbits(x):
%o A280971     if(x<2):
%o A280971         return (0,0);
%o A280971     s=0;t=0
%o A280971     f=list(factor(x));
%o A280971     #ensures inequality of numfactorbits(x) and bin(x).count("1") if x is prime
%o A280971     if((len(f)==1)&(f[0][1]==1)):
%o A280971         return (0,0);
%o A280971     for c in range(len(f)):
%o A280971         s+=bin(f[c][0]).count("1")*f[c][1]
%o A280971         t+=(bin(f[c][0]).count("0")-1)*f[c][1]
%o A280971     return (s,t);
%o A280971 counter=2
%o A280971 index=1
%o A280971 while(index<=10000):
%o A280971     if(factorbits(counter)==(bin(counter).count("1"),bin(counter).count("0")-1)):
%o A280971         print(str(index)+" "+str(counter))
%o A280971         index+=1;
%o A280971     counter+=1;
%o A280971 (Python)
%o A280971 from sympy import factorint
%o A280971 def ok(n):
%o A280971     f = factorint(n)
%o A280971     return sum(f.values()) > 1 and sorted(bin(n)[2:]) == sorted("".join(bin(p)[2:]*f[p] for p in f))
%o A280971 print([k for k in range(5000) if ok(k)]) # _Michael S. Branicky_, Apr 20 2025
%Y A280971 Cf. A278909, A280967, A280928.
%K A280971 nonn,base
%O A280971 1,1
%A A280971 _Ely Golden_, Jan 11 2017