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

Author

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

Keywords

• nonn
• easy

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.

Crossrefs

Cf. A037916, A046523, A101296, A118914.

Programs

PARI

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