login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A009223
a(n) = gcd(sigma(n), phi(n)).
25
1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 4, 2, 6, 8, 1, 2, 3, 2, 2, 4, 2, 2, 4, 1, 6, 2, 4, 2, 8, 2, 1, 4, 2, 24, 1, 2, 6, 8, 2, 2, 12, 2, 4, 6, 2, 2, 4, 3, 1, 8, 2, 2, 6, 8, 24, 4, 2, 2, 8, 2, 6, 4, 1, 12, 4, 2, 2, 4, 24, 2, 3, 2, 6, 4, 4, 12, 24, 2, 2, 1, 2, 2, 8, 4, 6, 8, 20, 2, 6, 8, 4, 4, 2, 24, 4, 2, 3, 12, 1, 2, 8
OFFSET
1,3
COMMENTS
The asymptotic density of numbers k such that a(k) <= m for a given m is 0 (Dressler, 1974). - Amiram Eldar, Mar 02 2021
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Robert E. Dressler, On a theorem of Niven, Canadian Mathematical Bulletin, Vol. 17, No. 1 (1974), pp. 109-110.
FORMULA
a(n) = gcd(A000203(n), A000010(n)).
MATHEMATICA
Table[GCD[DivisorSigma[1, n], EulerPhi[n]], {n, 110}] (* Harvey P. Dale, Aug 10 2011 *)
PROG
(PARI) a(n)=gcd(sigma(n=factor(n)), eulerphi(n)) \\ Charles R Greathouse IV, Nov 27 2013
(Haskell)
a009223 n = gcd (a000203 n) (a000010 n)
-- Reinhard Zumkeller, Jan 19 2014
CROSSREFS
Cf. A000010 (phi), A000203 (sigma).
Sequence in context: A082064 A082055 A073812 * A110244 A309020 A278495
KEYWORD
nonn
STATUS
approved