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

1,1

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.

Links

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

Example

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

Prog

(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")
(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

Crossrefs

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

Cf. A176670

Sequence in context: A062693 A067203 A230544 * A080718 A219993 A237562

Adjacent sequences: A280925 A280926 A280927 * A280929 A280930 A280931

Keyword

nonn,base

Author

Ely Golden, Jan 11 2017

Status

approved