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

1,2

Comments

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

Links

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

Formula

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

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Cf. also A099635, A099636.

Sequence in context: A243731 A334945 A273825 * A081806 A059806 A332425

Adjacent sequences: A082296 A082297 A082298 * A082300 A082301 A082302

Keyword

nonn

Author

Reinhard Zumkeller, Apr 08 2003

Status

approved