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

1255, 12955, 17482, 25105, 100255, 101299, 105295, 107329, 117067, 124483, 127417, 129595, 132565, 145273, 146137, 149782, 163797, 174082, 174298, 174793, 174982, 250105, 256315, 263155, 295105, 297463, 307183, 325615, 371893, 536539, 687919, 1002955, 1004251, 1012099, 1025095, 1029955

Offset: 1

Author

Ely Golden, Jan 11 2017

Keywords

• nonn
• base

Comments

Subsequence of A176670 as well as A020342.

Is this sequence the intersection of A176670 and A020342?

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.

Examples

			100255 is a member of this sequence as 100255 = 5*20051, which is exactly the same set of digits as 100255.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..3643 from Ely Golden)

Crossrefs

The following sequences are all closely related: A020342, A014575, A080718, A280928, A048936, A144563.

Cf. A176670

Programs

Python

from sympy import factorint
def ok(n):
    f = factorint(n)
    return sum(f.values()) > 1 and sorted(str(n)) == sorted("".join(str(p)*f[p] for p in f))
print([k for k in range(700000) if ok(k)]) # Michael S. Branicky, Apr 20 2025

SageMath

def digits(x, n):
    if((x<=0)|(n<2)):
        return []
    li=[]
    while(x>0):
        d=divmod(x, n)
        li.append(d[1])
        x=d[0]
    li.sort()
    return li;
def factorDigits(x, n):
    if((x<=0)|(n<2)):
        return []
    li=[]
    f=list(factor(x))
    #ensures inequality of digits(x, n) and factorDigits(x, n) if x is prime
    if((len(f)==1)&(f[0][1]==1)):
        return [];
    for c in range(len(f)):
        for d in range(f[c][1]):
            ld=digits(f[c][0], n)
            li+=ld
    li.sort()
    return li;
#this variable affects the radix
radix=10
c=2
index=1
while(index<=100):
    if(digits(c,radix)==factorDigits(c,radix)):
        print(str(index)+" "+str(c))
        index+=1
    c+=1
print("complete")