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Search: id:A005361
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| A005361 |
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Product of exponents of prime factorization of n.
(Formerly M0063)
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+0
18
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| 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 3, 2, 1, 1, 1, 5, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 4, 2, 2, 1, 2, 1, 3, 1, 3, 1, 1, 1, 2, 1, 1, 2, 6, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 2, 2, 1, 1
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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a(n) depends only on prime signature of n (cf. A025487). So a(24) = a(375) since 24=2^3*3 and 375 =3*5^3 both have prime signature (3,1).
a(n) is the number of nilpotents elements in the ring Z/nZ. - Roger Cuculiere (cuculier(AT)imaginet.fr), Jan 02 2004
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REFERENCES
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Problem 5735, Amer. Math. Monthly, 78 (1971), 680-681.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
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FORMULA
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n = Product (p_j^k_j) -> a(n) = Product (k_j). Dirichlet g.f.: zeta(s)*zeta(2s)*zeta(3s)/zeta(6s).
Multiplicative with a(p^e) = e. - David W. Wilson (davidwwilson(AT)comcast.net), Aug 01, 2001.
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MATHEMATICA
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Prepend[ Array[ Times @@ Last[ Transpose[ FactorInteger[ # ] ] ]&, 100, 2 ], 1 ]
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PROGRAM
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(PARI) for(n=1, 100, print1(prod(i=1, omega(n), component(component(factor(n), 2), i)), ", "))
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CROSSREFS
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Cf. A000005, A052306. a(p^k)=A000027=n. a(A002110)=A000012=1.
Sequence in context: A051903 A072411 A091050 this_sequence A008479 A107345 A000688
Adjacent sequences: A005358 A005359 A005360 this_sequence A005362 A005363 A005364
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KEYWORD
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nonn,easy,nice,mult
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AUTHOR
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Jeffrey Shallit, Olivier Gerard (ogerard(AT)ext.jussieu.fr)
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