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%I #23 Mar 03 2023 11:12:45
%S 0,1,1,2,1,11,1,3,2,11,1,12,1,11,11,4,1,12,1,12,11,11,1,13,2,11,3,12,
%T 1,111,1,5,11,11,11,22,1,11,11,13,1,111,1,12,12,11,1,14,2,12,11,12,1,
%U 13,11,13,11,11,1,112,1,11,12,6,11,111,1,12,11,111,1,23,1,11,12,12,11,111
%N a(n) = Sum_{i=1..m} e(i) * 10^(m-i) where e(1) <= ... <= e(m) are the nonzero exponents in the prime factorization of n: a representation of the prime signature of n.
%C The sorted sequence of (nonzero) exponents in the prime factorization of a number is called its prime signature. Here this is "approximated" by multiplying them by powers of 10. Up to 2^10 this coincides with the concatenation of these exponents written in base 10 (but that sequence would be "base" specific).
%C For n >= 1024 one should use a modified definition, replacing 10 with 10^floor(1+log_10(log_2(n))), to avoid ambiguity of the representation.
%H Antti Karttunen, <a href="/A139393/b139393.txt">Table of n, a(n) for n = 1..1023</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeSignature.html">Prime Signature</a>.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Prime_signature">Prime signature</a>.
%o (PARI) A139393(n)=sum(i=1,#n=vecsort(factor(n)[,2]),10^(#n-i)*n[i])
%Y Cf. A037916, A046523, A101296, A118914.
%K nonn,easy
%O 1,4
%A _M. F. Hasler_, Apr 17 2008, Apr 19 2008
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