login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A161606 a(n) = gcd(A008472(n), A001222(n)). 2

%I

%S 0,1,1,2,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,1,2,1,1,1,1,1,3,3,1,1,1,1,2,1,

%T 2,1,1,1,2,1,1,3,1,1,1,1,1,5,1,1,2,3,1,1,2,1,2,1,1,2,1,1,1,2,2,1,1,1,

%U 2,1,1,5,1,1,1,3,2,3,1,1,1,1,1,4,2,1,2,1,1,2,2,1,2,1,2,1,1,3,1,1,1,1,1,1,3

%N a(n) = gcd(A008472(n), A001222(n)).

%H Antti Karttunen, <a href="/A161606/b161606.txt">Table of n, a(n) for n = 1..10000</a>

%e 28 has a prime-factorization of: 2^2 * 7^1. The sum of the distinct primes dividing 28 is 2+7 = 9. The sum of the exponents in the prime-factorization of 28 is 2+1 = 3. a(28) therefore equals gcd(9,3) = 3.

%p A008472 := proc(n) if n = 1 then 0 ; else add(p, p= numtheory[factorset](n)) ; end if ; end proc:

%p A161606 := proc(n) igcd(A008472(n),numtheory[bigomega](n)) ; end proc:

%p seq(A161606(n),n=2..80) ; # _R. J. Mathar_, Jul 08 2011

%t Table[GCD[DivisorSum[n, # &, PrimeQ], PrimeOmega@ n], {n, 105}] (* _Michael De Vlieger_, Jul 20 2017 *)

%o (Scheme) (define (A161606 n) (gcd (A001222 n) (A008472 n))) ;; _Antti Karttunen_, Jul 20 2017

%o (Python)

%o from sympy import primefactors, gcd

%o def a001222(n): return 0 if n==1 else a001222(n/primefactors(n)[-1]) + 1

%o def a(n): return gcd(sum(primefactors(n)), a001222(n))

%o print map(a, range(1, 151)) # _Indranil Ghosh_, Jul 20 2017

%Y Cf. A001222, A008472.

%K nonn

%O 1,4

%A _Leroy Quet_, Jun 14 2009

%E Term a(1)=0 prepended and more terms computed by _Antti Karttunen_, Jul 20 2017

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 6 23:01 EDT 2020. Contains 335484 sequences. (Running on oeis4.)