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Search: id:A076109
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| A076109 |
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Least positive k such that k^n is the sum of n consecutive integers, or 0 if no such k exists. |
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+0
3
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| 1, 1, 3, 0, 5, 3, 7, 0, 3, 5, 11, 0, 13, 7, 15, 0, 17, 3, 19, 0, 21, 11, 23, 0, 5, 13, 3, 0, 29, 15, 31, 0, 33, 17, 35, 0, 37, 19, 39, 0, 41, 21, 43, 0, 15, 23, 47, 0, 7, 5, 51, 0, 53, 3, 55, 0, 57, 29, 59, 0, 61, 31, 21, 0, 65, 33, 67, 0, 69, 35, 71, 0, 73, 37, 15, 0, 77, 39, 79, 0
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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No k exists precisely when n == 0 (mod 4).
a(p) = p if p is a prime.
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FORMULA
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a(n) = (n*A076107(n)+(n^2-n)/2)^(1/n) for n != 0 (mod 4).
a(n) = A076108^(1/n).
Multiplicative with a(2^1) = 1; a(2^e) = 0 if e >= 2; a(p^e) = p if p >= 3. - David W. Wilson, Jun 10 2005
a(n) = A007947(n) if n == 1 (mod 2); A007947(n/2) if n == 2 (mod 4); 0 if n == 0 (mod 4). - David W. Wilson, Jun 10 2005
a(4k)=0; otherwise a(n)=p1*...*pm where p1, ..., pm are all distinct odd primes dividing n. - Max Alekseyev (maxal(AT)cs.ucsd.edu), Jun 10 2005
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PROGRAM
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(PARI) for(n=1, 100, t=n*(n-1)/2:f=0:for(r=1, 10^4, if((r^n-t)%n==0, f=r:break)):print1(f", "))
(PARI) {A076109(n)=if(n%4==0, return(0)); if(n%2==0, n\=2); f=factorint(n)[, 1]; prod(i=1, length(f), f[i])} (Alekseyev)
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CROSSREFS
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Cf. A076107, A076108.
Sequence in context: A011293 A088191 A108500 this_sequence A078788 A005069 A037284
Adjacent sequences: A076106 A076107 A076108 this_sequence A076110 A076111 A076112
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KEYWORD
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nonn,mult
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Oct 08 2002
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EXTENSIONS
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Corrected and extended by Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 30 2003
More terms from Max Alekseyev (maxal(AT)cs.ucsd.edu), Jun 10 2005
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