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A248915
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Composite numbers which divide the concatenation of their prime factors, with multiplicity, in descending order.
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5
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OFFSET
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1,1
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COMMENTS
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Prime numbers are not considered because they trivially satisfy the relation.
a(2), the bound for a(9) above, and larger terms may be found using an extension of Andersen's algorithm to arbitrary base and ordering (see links for an implementation and another term). - Michael S. Branicky, Apr 13 2024
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LINKS
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EXAMPLE
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Prime factors of 378 are 2,3,3,3,7; concat(7,3,3,3,2) = 73332 and 73332/378 = 194.
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MAPLE
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with(numtheory); P:=proc(q) local a, b, c, d, j, k, n;
for n from 1 to q do if not isprime(n) then a:=ifactors(n)[2]; b:=[]; d:=0;
for k from 1 to nops(a) do b:=[op(b), a[k][1]]; od; b:=sort(b);
for k from nops(a) by -1 to 1 do c:=1; while not b[k]=a[c][1] do c:=c+1; od;
for j from 1 to a[c][2] do d:=10^(ilog10(b[k])+1)*d+b[k]; od; od;
if type(d/n, integer) then print(n); fi;
fi; od; end: P(10^9);
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PROG
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(PARI) isok(n) = {my(s = ""); my(f = factor(n)); forstep (i=#f~, 1, -1, for (k=1, f[i, 2], s = concat(s, Str(f[i, 1])))); (eval(s) % n) == 0; } \\ Michel Marcus, Jun 16 2015
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CROSSREFS
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KEYWORD
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nonn,more,base,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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