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Search: id:A076107
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| A076107 |
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First of n consecutive integers whose sum is a positive n-th power, or 0 if no such integers exist. |
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+0
3
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| 1, 0, 8, 0, 623, 119, 117646, 0, 2183, 976558, 25937424596, 0, 23298085122475, 48444505197, 29192926025390618, 0, 48661191875666868473, 21523352, 104127350297911241532832, 0, 278218429446951548637196391
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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No sum exists precisely when n == 0 (mod 4). a(2) = 0 is a legitimate value.
The sum is given by A076108(n) = A076109(n)^n for n != 0 (mod 4).
a(p) = p^(p-1)-(p-1)/2 for prime p.
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FORMULA
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a(n) = A076108(n)/n-(n-1)/2 for n != 0 (mod 4).
a(4k)=0; otherwise a(n) = (2*A076108(n)/n - n + 1)/2 = (2*p1^n*...*pm^n/n - n + 1)/2 where p1, ..., pm are all distinct odd primes dividing n. - Max Alekseyev (maxal(AT)cs.ucsd.edu), Jun 10 2005
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EXAMPLE
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a(3) = 8 as 8+9+10 = 27 = 3^3. a(6) = 119 as 119+120+..+124 = 729 = 3^6.
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PROGRAM
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(PARI) for(n=1, 30, t=n*(n-1)/2:f=0:for(r=1, 10^4, if((r^n-t)%n==0, f=(r^n-t)/n:break)):print1(f", "))
(PARI) {A076107(n)=if(n%4==0, return(0)); m=n; if(m%2==0, m\=2); f=factorint(m)[, 1]; p=1; (2*prod(i=1, length(f), f[i])^n/n-n+1)/2} (Alekseyev)
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CROSSREFS
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Cf. A076108, A076109.
Sequence in context: A121770 A013376 A013456 this_sequence A076952 A094922 A088990
Adjacent sequences: A076104 A076105 A076106 this_sequence A076108 A076109 A076110
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KEYWORD
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nonn
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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
Revised by Max Alekseyev (maxal(AT)cs.ucsd.edu) and David W. Wilson, Jun 10 2005
More terms from Max Alekseyev (maxal(AT)cs.ucsd.edu), Jun 10 2005
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