A066452 Anti-phi(n).

1, 1, 2, 1, 4, 1, 4, 4, 3, 2, 8, 3, 7, 7, 9, 2, 8, 5, 10, 10, 8, 6, 19, 6, 12, 9, 9, 8, 22, 9, 12, 12, 15, 10, 31, 9, 11, 14, 24, 13, 23, 9, 24, 17, 16, 10, 35, 15, 23, 25, 20, 12, 40, 17, 34, 21, 18, 14, 37, 17, 24, 25, 41, 20, 39, 14, 31, 34, 33, 18, 42, 16, 32, 37, 41, 18, 44, 25

Offset: 2

Author

Jon Perry, Dec 29 2001

Keywords

• nonn
• easy

Comments

anti-phi(n) = the number of integers < n that are not divisible by any anti-divisor of n.

The old definition given for this sequence was: anti-phi(n) = number of integers <= n that are coprime to the anti-divisors of n. However this does not match the entries.

See A066272 for definition of anti-divisor.

Examples

			10 has anti-divisors 3,4,7. The numbers not divisible by any of 3,4,7 and less than 10 are 1,2,5. Therefore anti-phi(10)=3.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 2..10000 [This replaces an earlier b-file computed by Diana Mecum]
• Jon Perry, Anti-phi function [Broken link]
• Jon Perry, The Anti-divisor [Cached copy]
• Jon Perry, The Anti-divisor: Even More Anti-Divisors [Cached copy]

Crossrefs

Cf. A058838, A066241.

Programs

Maple

# needs antidivisors() as implemented in A066272
A066452 := proc(n)local ad,isad,j,k,totad:ad:=antidivisors(n):totad:=0:for j from 1 to n-1 do isad:=1:for k from 1 to nops(ad) do if(j mod ad[k]=0)then isad:=0:break: fi:od:totad:=totad+isad:od:return totad:end:
seq(A066452(n), n=2..50); # Nathaniel Johnston, Apr 20 2011

PARI

antidiv(n) = {my(v = []); for (k=2, n-1, if (abs((n % k) - k/2) < 1, v = concat(v, k));); v;}
a(n) = {my(vad = antidiv(n)); my(nbad = 0); for (j=1, n-1, isad = 1; for (k=1, #vad, if ((j % vad[k]) == 0, isad = 0; break); ); nbad += isad;); nbad;} \\ Michel Marcus, Feb 25 2016

Python

def A066452(n):
    return len([x for x in range(1,n) if all([x % d  for d in range(2,n) if (n % d) and (2*n) % d in [d-1,0,1]])]) # Chai Wah Wu, Aug 07 2014

Extensions

Better definition and more terms from Diana L. Mecum, Jul 01 2007