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A133482
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a(p_1^e_1*p_2^e_2*.....*p_m^e_m) = (p_1^p_1)^e_1*(p_2^p^2)^e_2*.....*(p_m^p_m)^e_m where p_1^e_1*p_2^e_2*.....*p_m^e_m is the prime decomposition of n.
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2
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1, 4, 27, 16, 3125, 108, 823543, 64, 729, 12500, 285311670611, 432, 302875106592253, 3294172, 84375, 256, 827240261886336764177, 2916, 1978419655660313589123979, 50000, 22235661, 1141246682444, 20880467999847912034355032910567, 1728, 9765625, 1211500426369012, 19683, 13176688, 2567686153161211134561828214731016126483469, 337500
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Totally multiplicative sequence with a(p) = p^p for prime p. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Oct 17 2009]
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FORMULA
| Multiplicative with a(p^e) = p^(pe). If n = Product p(k)^e(k) then a(n) = Product p(k)^(p(k)*e(k)). [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Oct 17 2009]
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EXAMPLE
| a(6)=a(2^1*3^1)=2^2^1*3^3^1=4*27=108
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MAPLE
| A133482 := proc(n) local ifs, f ; if n = 1 then 1; else ifs := ifactors(n)[2] ; mul( (op(1, f)^op(1, f))^op(2, f), f=ifs) ; fi ; end: seq(A133482(n), n=1..30) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 30 2007
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CROSSREFS
| Sequence in context: A136511 A108138 A119361 * A108139 A200768 A176147
Adjacent sequences: A133479 A133480 A133481 * A133483 A133484 A133485
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KEYWORD
| nonn,mult
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AUTHOR
| Masahiko Shin (nin-ts5406(AT)w9.dion.ne.jp), Nov 29 2007
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EXTENSIONS
| Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 30 2007
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