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A056624 Number of unitary square divisors of n. 4
1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 4, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Unitary analog of A046951.

LINKS

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

Index entries for sequences computed from exponents in factorization of n

FORMULA

a(n) = 2^r, where r is the number of prime factors of the largest unitary square divisor of n.

Multiplicative with a(p^e) = 2^(1-(e mod 2)). - Vladeta Jovovic, Dec 13 2002

EXAMPLE

n=256, it has 5 square divisors of which only 2,{1,256} are unitary, 3 divisors are not.

n=124 has 2 (1 and 4) square divisors, both of them unitary a(124) = 2.

n=108 has 12 divisors, 4 square divisors: {1,4,9,36} of which 1 and 4 are unitary, 9 and 36 are not. So a(108)=2. The largest unitary square divisor of 108 is 4 with 1 prime divisor so a(108) = 2^1 = 2.

MATHEMATICA

Table[DivisorSum[n, 1 &, And[IntegerQ@ Sqrt@ #, CoprimeQ[#, n/#]] &], {n, 105}] (* Michael De Vlieger, Jul 28 2017 *)

PROG

(Scheme) (define (A056624 n) (if (= 1 n) n (* (A000079 (A059841 (A067029 n))) (A056624 (A028234 n))))) ;; Antti Karttunen, Jul 28 2017

(PARI) a(n) = sumdiv(n, d, if(gcd(d, n/d)==1, issquare(d))); \\ Michel Marcus, Jul 28 2017

CROSSREFS

Cf. A000188, A008833, A034444, A046952, A055229, A056626, A059841.

Sequence in context: A277231 A122934 A072170 * A193348 A263723 A093997

Adjacent sequences:  A056621 A056622 A056623 * A056625 A056626 A056627

KEYWORD

nonn,mult

AUTHOR

Labos Elemer, Aug 08 2000

EXTENSIONS

More terms from Vladeta Jovovic, Dec 13 2002

STATUS

approved

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Last modified September 20 03:18 EDT 2017. Contains 292251 sequences.