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A089723
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a(1)=1, for n>1; a(n) gives number of ways to write n as n = x^y, 2 <= x, 1 <= y.
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3
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1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| This function depends only on the prime signature of n. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 10 2006
a(n) = number of perfect divisors of n. Perfect divisor of n is divisor d such that d^k = n for some k >= 1. a(n) > 1 for perfect powers n = A001597(m) for m > 2. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Jan 23 2010]
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LINKS
| S. W. Golomb, A new arithmetic function of combinatorial significance J. Number Theory 5 (1973) 218-223. 1973JNT.....5..218G
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FORMULA
| If n = Product p_i^e_i, a(n) = d(gcd(<e_i>)). - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 10 2006
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EXAMPLE
| 144 = 2^4 * 3^2, gcd(4,2) = 2, d(2) = 2, so a(144) = 2. The representations are 144^1 and 12^2.
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CROSSREFS
| Cf. A000005.
Sequence in context: A037827 A086074 A180601 * A055215 A058398 A091499
Adjacent sequences: A089720 A089721 A089722 * A089724 A089725 A089726
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KEYWORD
| easy,nonn,changed
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AUTHOR
| Naohiro Nomoto (pcmusume(AT)m11.alpha-net.ne.jp), Jan 07 2004
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