A037916 Concatenate exponents in prime factorization of n.

0, 1, 1, 2, 1, 11, 1, 3, 2, 11, 1, 21, 1, 11, 11, 4, 1, 12, 1, 21, 11, 11, 1, 31, 2, 11, 3, 21, 1, 111, 1, 5, 11, 11, 11, 22, 1, 11, 11, 31, 1, 111, 1, 21, 21, 11, 1, 41, 2, 12, 11, 21, 1, 13, 11, 31, 11, 11, 1, 211, 1, 11, 21, 6, 11, 111, 1, 21, 11, 111, 1, 32, 1, 11, 12, 21, 11, 111

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Comments

a(n) = 1 for prime n; a(n) = 11, 111, 1111, ... if n = product of two, three, four, ... distinct primes. - Zak Seidov, Dec 15 2006

The sequence of (nonzero) exponents in the prime factorization of n, sorted in decreasing order, is called the prime signature of n, cf. A124010. - M. F. Hasler, Apr 17 2008, edited Oct 12 2018

Examples

			12 = 2^2 * 3^1, so a(12) = 21.
		

Links

• Zak Seidov and Michael De Vlieger, Table of n, a(n) for n = 1..10000 (First 2000 terms from Zak Seidov)
• Wikipedia, Prime signature.

Crossrefs

Cf. A124010, A139393, A320390.

Programs

Mathematica

Join[{0},Table[FromDigits[Flatten[IntegerDigits/@Transpose[ FactorInteger[ n]][[2]]]],{n,2,80}]] (* Harvey P. Dale, Sep 29 2012 *)

PARI

A037916(n)=if( n>1, eval(concat(concat([""],factor(n)[,2]~)))) \\ M. F. Hasler, Apr 17 2008

Python

from sympy import factorint
def a(n): return 0 if n<2 else int("".join(map(str, factorint(n).values())))
print([a(n) for n in range(1, 79)]) # Michael S. Branicky, Mar 18 2021

Extensions

More terms from Erich Friedman