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A037916
Concatenate exponents in prime factorization of n.
16
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
KEYWORD
nonn,base,easy
EXTENSIONS
More terms from Erich Friedman
STATUS
approved