cp's OEIS Frontend

A280928 Composite numbers having the same digits as their prime factors (with multiplicity), including zero digits.

%I A280928 #21 Apr 24 2025 17:34:34
%S A280928 1255,12955,17482,25105,100255,101299,105295,107329,117067,124483,
%T A280928 127417,129595,132565,145273,146137,149782,163797,174082,174298,
%U A280928 174793,174982,250105,256315,263155,295105,297463,307183,325615,371893,536539,687919,1002955,1004251,1012099,1025095,1029955
%N A280928 Composite numbers having the same digits as their prime factors (with multiplicity), including zero digits.
%C A280928 Subsequence of A176670 as well as A020342.
%C A280928 Is this sequence the intersection of A176670 and A020342?
%C A280928 Excluding 1, all members of A080718 are members of this sequence. The first member of this sequence that is not a member of A080718 is a(17)=163797.
%H A280928 Michael S. Branicky, <a href="/A280928/b280928.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..3643 from Ely Golden)
%e A280928 100255 is a member of this sequence as 100255 = 5*20051, which is exactly the same set of digits as 100255.
%o A280928 (SageMath)
%o A280928 def digits(x, n):
%o A280928     if((x<=0)|(n<2)):
%o A280928         return []
%o A280928     li=[]
%o A280928     while(x>0):
%o A280928         d=divmod(x, n)
%o A280928         li.append(d[1])
%o A280928         x=d[0]
%o A280928     li.sort()
%o A280928     return li;
%o A280928 def factorDigits(x, n):
%o A280928     if((x<=0)|(n<2)):
%o A280928         return []
%o A280928     li=[]
%o A280928     f=list(factor(x))
%o A280928     #ensures inequality of digits(x, n) and factorDigits(x, n) if x is prime
%o A280928     if((len(f)==1)&(f[0][1]==1)):
%o A280928         return [];
%o A280928     for c in range(len(f)):
%o A280928         for d in range(f[c][1]):
%o A280928             ld=digits(f[c][0], n)
%o A280928             li+=ld
%o A280928     li.sort()
%o A280928     return li;
%o A280928 #this variable affects the radix
%o A280928 radix=10
%o A280928 c=2
%o A280928 index=1
%o A280928 while(index<=100):
%o A280928     if(digits(c,radix)==factorDigits(c,radix)):
%o A280928         print(str(index)+" "+str(c))
%o A280928         index+=1
%o A280928     c+=1
%o A280928 print("complete")
%o A280928 (Python)
%o A280928 from sympy import factorint
%o A280928 def ok(n):
%o A280928     f = factorint(n)
%o A280928     return sum(f.values()) > 1 and sorted(str(n)) == sorted("".join(str(p)*f[p] for p in f))
%o A280928 print([k for k in range(700000) if ok(k)]) # _Michael S. Branicky_, Apr 20 2025
%Y A280928 The following sequences are all closely related: A020342, A014575, A080718, A280928, A048936, A144563.
%Y A280928 Cf. A176670
%K A280928 nonn,base
%O A280928 1,1
%A A280928 _Ely Golden_, Jan 11 2017