A129138 a(n) = number of positive divisors of n that are <= phi(n), where phi(n) = A000010(n).

1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 4, 1, 2, 3, 4, 1, 4, 1, 4, 3, 2, 1, 6, 2, 2, 3, 4, 1, 5, 1, 5, 3, 2, 3, 7, 1, 2, 3, 6, 1, 5, 1, 4, 5, 2, 1, 8, 2, 4, 3, 4, 1, 6, 3, 6, 3, 2, 1, 9, 1, 2, 5, 6, 3, 5, 1, 4, 3, 6, 1, 10, 1, 2, 5, 4, 3, 5, 1, 8, 4, 2, 1, 9, 3, 2, 3, 6, 1, 9, 3, 4, 3, 2, 3, 10, 1, 4, 5, 7, 1, 5, 1, 6

Offset

1,4

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

phi(16) = 8. So a(16) is the number of divisors of 16 which are <= 8. There are 4 such divisors: 1, 2, 4, 8; so a(16) = 4.

Maple

with(numtheory): a:=proc(n) local div, ct, j: div:=divisors(n): ct:=0: for j from 1 to tau(n) do if div[j]<=phi(n) then ct:=ct+1 else ct:=ct: fi od: ct; end: seq(a(n), n=1..135); # Emeric Deutsch, Mar 31 2007

Mathematica

Table[Length[Select[Divisors[n], # <= EulerPhi[n] &]], {n, 104}] (* Jayanta Basu, May 23 2013 *)

Prog

(PARI) a(n)=my(p=eulerphi(n)); #select(k->k<=p, divisors(n)) \\ Charles R Greathouse IV, Mar 05 2013

Crossrefs

Cf. A129139, A126131, A074919.

Sequence in context: A320266 A277692 A354992 * A353378 A112970 A112971

Adjacent sequences: A129135 A129136 A129137 * A129139 A129140 A129141

Keyword

nonn

Author

Leroy Quet, Mar 30 2007

Extensions

More terms from Emeric Deutsch, Mar 31 2007

Status

approved