A140747 a(n) is the number of divisors of n that are coprime to the next larger divisor of n.

0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 1, 2, 1, 4, 1, 1, 2, 2, 2, 3, 1, 2, 2, 3, 1, 3, 1, 2, 3, 2, 1, 3, 1, 2, 2, 2, 1, 2, 2, 3, 2, 2, 1, 5, 1, 2, 3, 1, 2, 3, 1, 2, 2, 4, 1, 4, 1, 2, 2, 2, 2, 3, 1, 3, 1, 2, 1, 5, 2, 2, 2, 2, 1, 5, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 1, 3, 1, 2, 4

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

a(n) + A140748(n) = A000005(n) - 1.

Example

The divisors of 20 are 1,2,4,5,10,20. 1 is coprime to 2. 2 is not coprime to 4. 4 is coprime to 5. 5 is not coprime to 10. And 10 is not coprime to 20. So there are 2 divisors, 1 and 4, that are each coprime to the next higher divisor. So a(20) = 2.

Prog

(PARI) A140747(n) = { my(s=0, pd=0); fordiv(n, d, s += (pd&&(1==gcd(d, pd))); pd = d); s; }; \\ (Based on the fact that in PARI, if the first argument of fordiv is an integer, divisors are sorted by increasing size.) Antti Karttunen, Aug 12 2017

Crossrefs

Cf. A000005, A136164, A136165, A136166, A136167, A140748.

Sequence in context: A206921 A327402 A123529 * A330757 A322373 A332288

Adjacent sequences: A140744 A140745 A140746 * A140748 A140749 A140750

Keyword

nonn

Author

Leroy Quet, May 26 2008

Extensions

Extended by Max Alekseyev, Mar 12 2009

Status

approved