A082299 Greatest common divisor of n and its sum of prime factors (with repetition).

1, 2, 3, 4, 5, 1, 7, 2, 3, 1, 11, 1, 13, 1, 1, 8, 17, 2, 19, 1, 1, 1, 23, 3, 5, 1, 9, 1, 29, 10, 31, 2, 1, 1, 1, 2, 37, 1, 1, 1, 41, 6, 43, 1, 1, 1, 47, 1, 7, 2, 1, 1, 53, 1, 1, 1, 1, 1, 59, 12, 61, 1, 1, 4, 1, 2, 67, 1, 1, 14, 71, 12, 73, 1, 1, 1, 1, 6, 79, 1, 3, 1, 83, 14, 1, 1, 1, 1, 89, 1, 1, 1, 1

Offset: 1

Author

Reinhard Zumkeller, Apr 08 2003

Keywords

• nonn

Comments

For n > 4, a(n) = n iff n is prime.

Examples

			a(100) = GCD(2*2*5*5,2+2+5+5) = GCD(2*2*5,2*7) = 2;
a(200) = GCD(2*2*2*5*5,2+2+2+5+5) = GCD(2*2*2*5,2*2*2*2) = 8.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000 (first 1000 terms from Harvey P. Dale)

Crossrefs

Cf. A001414, A082300 (positions of ones), A082343, A082344.

Cf. also A099635, A099636.

Programs

Mathematica

Table[GCD[Total[Times@@@FactorInteger[n]],n],{n,100}] (* Harvey P. Dale, Dec 27 2015 *)

PARI

A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
A082299(n) = gcd(n, A001414(n)); \\ Antti Karttunen, Feb 01 2021

Formula

a(n) = gcd(n, A001414(n)).

a(n) = n / A082344(n) = A001414(n) / A082343(n). - Antti Karttunen, Feb 01 2021