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

1,4

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

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.

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A124010, A139393, A320390.

Sequence in context: A258055 A339306 A139393 * A320390 A292355 A262181

Adjacent sequences: A037913 A037914 A037915 * A037917 A037918 A037919

Keyword

nonn,base,easy

Author

N. J. A. Sloane

Extensions

More terms from Erich Friedman

Status

approved