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A072443
Nonsquares which are the product of two numbers with the same digits (leading zeros are forbidden).
3
252, 403, 574, 736, 765, 976, 1008, 1207, 1300, 1458, 1462, 1612, 1729, 1855, 1944, 2268, 2296, 2430, 2668, 2701, 2944, 3154, 3478, 3627, 3640, 4032, 4275, 4606, 4930, 5092, 5605, 5848, 6624, 6786, 7663, 8722, 11110, 12240, 13390, 13552, 14560, 14803, 15750, 16074
OFFSET
1,1
REFERENCES
P. Vaderlind, R. K. Guy and L. C. Larsen, The Inquisitive Problem Solver, Math. Assoc. Am., 2002, Problem P185.
LINKS
EXAMPLE
12*21 = 252 = 12*21, 403 = 13*31, 574 = 14*41, etc
PROG
(PARI) {for(n=100, 15000, k=floor(log(n)/log(100)); f=divisors(n); v=[]; for(h=1, matsize(f)[2], if(10^k<f[h]&&f[h]<10^(k+1), v=concat(v, f[h]))); b=matsize(v)[2]; if(b>1, w=[]; for(i=1, b, s=[]; a=v[i]; while(a>0, d=divrem(a, 10); a=d[1]; s=concat(d[2], s)); w=concat(w, [vecsort(s)])); c=0; for(i=1, b-1, for(j=i+1, b, if(c<1&&w[i]==w[j], if(v[i]*v[j]==n, print1(n, ", "); c=1))))))}
(Python)
from math import isqrt
from sympy import divisors
def ok(n): return isqrt(n)**2<n and any(sorted(str(d)) == sorted(str(n//d)) for d in divisors(n)[1:-1])
print([k for k in range(16100) if ok(k)]) # Michael S. Branicky, Sep 08 2024
CROSSREFS
A077760 is a subsequence.
Sequence in context: A372755 A104396 A207373 * A129623 A062904 A032800
KEYWORD
base,nonn
AUTHOR
N. J. A. Sloane, Nov 11 2002
EXTENSIONS
Extended by Klaus Brockhaus, Nov 12 2002
a(42) and beyond from Michael S. Branicky, Sep 08 2024
STATUS
approved