

A076109


Least positive k such that k^n is the sum of n consecutive integers, or 0 if no such k exists.


4



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
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OFFSET

1,3


COMMENTS

No k exists precisely when n == 0 (mod 4).
a(p) = p if p is a prime.


LINKS

Table of n, a(n) for n=1..80.


FORMULA

a(n) = (n*A076107(n)+(n^2n)/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, Jun 10 2005


PROG

(PARI) for(n=1, 100, t=n*(n1)/2:f=0:for(r=1, 10^4, if((r^nt)%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)


CROSSREFS

Cf. A076107, A076108.
Sequence in context: A179179 A291503 A108500 * A078788 A284599 A005069
Adjacent sequences: A076106 A076107 A076108 * A076110 A076111 A076112


KEYWORD

nonn,mult


AUTHOR

Amarnath Murthy, Oct 08 2002


EXTENSIONS

Corrected and extended by Ralf Stephan, Mar 30 2003
More terms from Max Alekseyev, Jun 10 2005


STATUS

approved



