login
A140748
a(n) is the number of divisors of n that are not coprime to the next larger divisor of n.
2
0, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 2, 0, 1, 1, 3, 0, 3, 0, 3, 1, 1, 0, 4, 1, 1, 2, 3, 0, 3, 0, 4, 1, 1, 1, 5, 0, 1, 1, 4, 0, 4, 0, 3, 2, 1, 0, 6, 1, 3, 1, 3, 0, 5, 1, 4, 1, 1, 0, 6, 0, 1, 2, 5, 1, 4, 0, 3, 1, 3, 0, 7, 0, 1, 3, 3, 1, 4, 0, 6, 3, 1, 0, 6, 1, 1, 1, 5, 0, 6, 1, 3, 1, 1, 1, 8, 0, 3, 3, 6, 0, 4, 0, 5, 3
OFFSET
1,8
LINKS
FORMULA
A140747(n) + a(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 3 divisors, 2, 5 and 10, that are each not coprime to the next higher divisor. So a(20) = 3.
PROG
(PARI) A140748(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
KEYWORD
nonn
AUTHOR
Leroy Quet, May 26 2008
EXTENSIONS
Extended by Max Alekseyev, Mar 12 2009
STATUS
approved