

A139393


a(n) = Sum_{i=1..m} e(i) * 10^(mi) where e(1) <= ... <= e(m) are the nonzero exponents in the prime factorization of n: a representation of the prime signature of n.


1



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, 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, 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
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OFFSET

1,4


COMMENTS

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).
For n >= 1024 one should use a modified definition, replacing 10 with 10^floor(1+log_10(log2(n))), to avoid ambiguity of the representation.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..1023
E. W. Weisstein, Prime signature on mathworld.wolfram.com.
Wikipedia, Prime signature.


PROG

(PARI) A139393(n)=sum(i=1, #n=vecsort(factor(n)[, 2]), 10^(#ni)*n[i])


CROSSREFS

Cf. A037916, A046523, A101296.
Sequence in context: A098290 A160110 A258055 * A037916 A320390 A292355
Adjacent sequences: A139390 A139391 A139392 * A139394 A139395 A139396


KEYWORD

nonn,easy,changed


AUTHOR

M. F. Hasler, Apr 17 2008, Apr 19 2008


STATUS

approved



