A280971 Composite numbers having the same bits as their prime factors (with multiplicity), including zero bits.
159, 287, 303, 319, 591, 623, 679, 687, 699, 763, 1135, 1167, 1203, 1243, 1247, 1271, 1351, 1371, 1391, 1631, 2167, 2173, 2231, 2285, 2319, 2359, 2463, 2471, 2495, 2519, 2743, 2779, 2787, 2809, 2863, 2931, 2933, 2991, 3029, 3039, 3503, 4223, 4279, 4287, 4319, 4343, 4411, 4439, 4479, 4487
Offset: 1
Links
- Ely Golden, Table of n, a(n) for n = 1..10000
Programs
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Python
from sympy import factorint def ok(n): f = factorint(n) return sum(f.values()) > 1 and sorted(bin(n)[2:]) == sorted("".join(bin(p)[2:]*f[p] for p in f)) print([k for k in range(5000) if ok(k)]) # Michael S. Branicky, Apr 20 2025 -
SageMath
def factorbits(x): if(x<2): return (0,0); s=0;t=0 f=list(factor(x)); #ensures inequality of numfactorbits(x) and bin(x).count("1") if x is prime if((len(f)==1)&(f[0][1]==1)): return (0,0); for c in range(len(f)): s+=bin(f[c][0]).count("1")*f[c][1] t+=(bin(f[c][0]).count("0")-1)*f[c][1] return (s,t); counter=2 index=1 while(index<=10000): if(factorbits(counter)==(bin(counter).count("1"),bin(counter).count("0")-1)): print(str(index)+" "+str(counter)) index+=1; counter+=1;
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