cp's OEIS Frontend

A037916 Concatenate exponents in prime factorization of n.

%I A037916 #34 Feb 20 2022 02:29:35
%S A037916 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,
%T A037916 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,
%U A037916 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
%N A037916 Concatenate exponents in prime factorization of n.
%C A037916 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
%C A037916 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
%H A037916 Zak Seidov and Michael De Vlieger, <a href="/A037916/b037916.txt">Table of n, a(n) for n = 1..10000</a> (First 2000 terms from Zak Seidov)
%H A037916 Wikipedia, <a href="http://en.wikipedia.org/wiki/Prime_signature">Prime signature</a>.
%e A037916 12 = 2^2 * 3^1, so a(12) = 21.
%t A037916 Join[{0},Table[FromDigits[Flatten[IntegerDigits/@Transpose[ FactorInteger[ n]][[2]]]],{n,2,80}]] (* _Harvey P. Dale_, Sep 29 2012 *)
%o A037916 (PARI) A037916(n)=if( n>1, eval(concat(concat([""],factor(n)[,2]~)))) \\ _M. F. Hasler_, Apr 17 2008
%o A037916 (Python)
%o A037916 from sympy import factorint
%o A037916 def a(n): return 0 if n<2 else int("".join(map(str, factorint(n).values())))
%o A037916 print([a(n) for n in range(1, 79)]) # _Michael S. Branicky_, Mar 18 2021
%Y A037916 Cf. A124010, A139393, A320390.
%K A037916 nonn,base,easy
%O A037916 1,4
%A A037916 _N. J. A. Sloane_
%E A037916 More terms from _Erich Friedman_