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A157195
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a(n) = 0 if n is 1 or a prime, otherwise a(n) = product of the proper divisors of n.
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1
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0, 0, 0, 2, 0, 6, 0, 8, 3, 10, 0, 144, 0, 14, 15, 64, 0, 324, 0, 400, 21, 22, 0, 13824, 5, 26, 27, 784, 0, 27000, 0, 1024, 33, 34, 35, 279936, 0, 38, 39, 64000, 0, 74088, 0, 1936, 2025, 46, 0, 5308416, 7, 2500, 51, 2704, 0, 157464, 55, 175616, 57, 58, 0, 777600000
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OFFSET
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1,4
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COMMENTS
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a(n) = 0 if and only if n is a noncomposite number (cf. A008578). - Omar E. Pol, Aug 01 2012
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LINKS
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FORMULA
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a(pq) = pq, p,q = distinct primes. a(p^k) = p^((1/2*k*(k-1)), p = prime, k = integer >=2. a(c) = A007955(c)/c, c = composite number.
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EXAMPLE
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For n = 15 a(15) = 15 = 3*5.
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MATHEMATICA
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If[#==1||PrimeQ[#], 0, Times@@Most[Divisors[#]]]&/@Range[60] (* Harvey P. Dale, Jan 24 2014 *)
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PROG
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(PARI) a(n) = {if ((n == 1) || isprime(n), return (0)); d = divisors(n); prod(i = 2, #d - 1, d[i]); } \\ Michel Marcus, Aug 05 2013
(Python)
from math import isqrt
from sympy import divisor_count
def A157195(n): return 0 if (c:=divisor_count(n)) <= 2 else (isqrt(n) if (c:=divisor_count(n)) & 1 else 1)*n**(c//2-1) # Chai Wah Wu, Jun 25 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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