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A196736 Define k(x) = number of m such that A000005(gcd(n,m)) is x where m runs from 1 to n , x = 1,2,.. ; z = A000005( cototient(n) ) ; sequence gives numbers n such that n - ( Sum_{i=1..j} k(i) ) divides cototient(n) for any j <= z , k(i)>0. 1
1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 23, 25, 27, 29, 31, 32, 33, 35, 37, 41, 43, 45, 47, 49, 51, 53, 59, 61, 63, 64, 65, 67, 71, 73, 75, 77, 79, 81, 83, 87, 89, 91, 95, 97, 99, 101, 103, 107, 109, 113, 119, 121, 123, 125, 127 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Sequence gives numbers n such that n - ( Sum_{i=1..j} k(i) ) are all distinct divisors of cototient(n) for all j <= z.

LINKS

Table of n, a(n) for n=1..60.

PROG

(Sage)

def is_A196736(n): # inefficient, for reference purposes

....k = lambda x: sum(1 for m in (1..n) if number_of_divisors(gcd(n, m))==x)

....cototient_n = n-euler_phi(n)

....z = number_of_divisors(cototient_n) if cototient_n > 0 else 0

....v = [(n-sum(k(i) for i in (1..j))) for j in (1..z)]

....return len(set(v)) == len(v) and all(vi.divides(cototient_n) for vi in v) # [D. S. McNeil, Oct 14 2011]

CROSSREFS

Sequence in context: A284676 A187681 A107750 * A284946 A285901 A246716

Adjacent sequences:  A196733 A196734 A196735 * A196737 A196738 A196739

KEYWORD

nonn

AUTHOR

Naohiro Nomoto, Oct 06 2011

STATUS

approved

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Last modified May 28 07:57 EDT 2017. Contains 287212 sequences.