A139393 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.

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

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(log_2(n))), to avoid ambiguity of the representation.

Links

Antti Karttunen, Table of n, a(n) for n = 1..1023

Eric Weisstein's World of Mathematics, Prime Signature.

Wikipedia, Prime signature.

Prog

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

Crossrefs

Cf. A037916, A046523, A101296, A118914.

Sequence in context: A160110 A258055 A339306 * A037916 A320390 A292355

Adjacent sequences: A139390 A139391 A139392 * A139394 A139395 A139396

Keyword

nonn,easy

Author

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

Status

approved