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A030628
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1 together with numbers of the form p*q^4 and p^9, where p and q are primes.
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9
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1, 48, 80, 112, 162, 176, 208, 272, 304, 368, 405, 464, 496, 512, 567, 592, 656, 688, 752, 848, 891, 944, 976, 1053, 1072, 1136, 1168, 1250, 1264, 1328, 1377, 1424, 1539, 1552, 1616, 1648, 1712, 1744, 1808, 1863, 1875, 2032, 2096, 2192, 2224, 2349, 2384
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also 1 together with numbers with 10 divisors. Also numbers n such that product of all proper divisors of n equals n^4.
If M(n) denotes the product of all divisors of n, then n is said to be k-multplicately perfect if M(n)=n^k. All such numbers are of the form p*q^(k-1) or p^(2k-1). The sequence A030628 is therefore 5-multiplicatively perfect. See the Links for A007422. - Walter A. Kehowski (wkehowski(AT)cox.net), Sep 13 2005
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REFERENCES
| D. M. Burton, Elementary Number Theory, Allyn and Bacon Inc., Boston, MA, 1976. p. 119.
David Wells, The Penguin Dictionary of Curious and Interesting Numbers, entry for 48, page 106, 1997.
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LINKS
| R. J. Mathar, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| Union A178739 U A179665 {1}. - R. J. Mathar, Apr 03 2011
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MAPLE
| with(numtheory): k:=5: MPL:=[]: for z from 1 to 1 do for n from 1 to 5000 do if convert(divisors(n), `*`) = n^k then MPL:=[op(MPL), n] fi od; od; MPL; (Kehowski)
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MATHEMATICA
| Join[{1}, Select[Range[6000], DivisorSigma[0, #]==10&]] (* From Vladimir Joseph Stephan Orlovsky, May 05 2011 *)
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PROG
| (PARI) {v=[]; for(n=1, 500, v=concat(v, if(numdiv(n)==10, n, ", ")); ); v} - Jason Earls Jun 18 2001
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CROSSREFS
| Cf. A030515, A030627, A030629.
Sequence in context: A143722 A110229 A108608 * A178739 A065911 A039426
Adjacent sequences: A030625 A030626 A030627 * A030629 A030630 A030631
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Jeff Burch (jmburch(AT)osprey.smcm.edu)
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EXTENSIONS
| Better description from Sharon Sela (sharonsela(AT)hotmail.com), Dec 23, 2001
More terms from Walter A. Kehowski (wkehowski(AT)cox.net), Sep 13 2005
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