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Search: id:A005934
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| A005934 |
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Highly powerful numbers.
(Formerly M3333)
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+0
13
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| 1, 4, 8, 16, 32, 64, 128, 144, 216, 288, 432, 864, 1296, 1728, 2592, 3456, 5184, 7776, 10368, 15552, 20736, 31104, 41472, 62208, 86400, 108000, 129600, 194400, 216000, 259200, 324000, 432000, 518400, 648000, 972000, 1296000, 1944000, 2592000
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
G. E. Hardy and M. V. Subbarao, Highly powerful numbers, Congress. Numer. 37 (1983), 277-307.
C. B. Lacampagne and J. L. Selfridge, Large highly powerful numbers are cubeful, Proc. Amer. Math. Soc., 91 (1984), 173-181.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..300
Index entries for sequences related to powerful numbers
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FORMULA
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For n = Prod p_i^e_i, let b(n) = Prod e_i; then n is highly powerful if b(n) sets a new record.
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PROGRAM
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(PARI) {prdex(n)=local(s, fac); s=1; fac=factor(n); for(k=1, matsize(fac)[1], s=s*fac[k, 2]); return(s)} {hp(m)=local(rec); rec=0; for(n=1, m, if(prdex(n)>rec, rec=prdex(n); print1(n", ")))}
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CROSSREFS
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Cf. A036965, A001694, A007532, A005934, A005188, A003321, A014576, A023052, A046074.
Cf. A085629
Adjacent sequences: A005931 A005932 A005933 this_sequence A005935 A005936 A005937
Sequence in context: A145108 A108569 A111073 this_sequence A085629 A046055 A020707
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Hardy and Subbarao give an extensive table.
Corrected and extended by Jason Earls (zevi_35711(AT)yahoo.com), Jul 10 2003
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