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A005729 a(n) is the smallest positive integer a for which there is an identity of the form a*x = Sum_{i=1..m} ai*gi(x)^n where a1, ..., am are in Z and g1(x), ..., gm(x) are in Z[x].
(Formerly M1557)
2
1, 1, 2, 6, 2, 60, 2, 42, 6, 30, 1, 660, 3, 364, 30, 42, 2, 1020, 1, 570, 42, 22, 1, 106260, 10, 390, 6, 1092, 1, 1740, 10, 1302, 66, 34, 70, 11220, 1, 1406, 78, 3990, 1, 223860, 1, 2838, 30, 46, 1, 4994220, 14, 210, 102, 390, 1, 54060, 110, 1092, 798, 58, 1, 21455940 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Previous name was: From polynomial identities.

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..60.

T. Chinburg and M. Henriksen, Sums of k-th powers in the ring of polynomials with integer coefficients, Bull. Amer. Math. Soc., 81 (1975), 107-110.

T. Chinburg and M. Henriksen, Sums of k-th powers in the ring of polynomials with integer coefficients, Acta Arithmetica, 29 (1976), 227-250.

FORMULA

a(n) = A005730(n)*A005731(n).

PROG

(PARI) expa(p, n) = {if (p % 2, return (1)); j = 2; expo = 1; while(2^j <= n+1, if (n % (2^j-1) == 0, expo = 2; break); j++); expo; }

expb(p, n) = {expo = 0; r = 1; ok = 1; while (ok, m = 2; while ((ps = (p^(m*r)-1)/(p^r-1)) <= n, if (n % ps == 0, expo = 1; break); m++; ); if (m==2, ok = 0); if (expo, break); r++; ); expo; }

expp(p, n) = if (n % p, expb(p, n), expa(p, n));

a(n) = {my(vp = primes(primepi(n-1))); prod(k=1, #vp, vp[k]^expp(vp[k], n)); } \\ Michel Marcus, Apr 27 2016

CROSSREFS

Cf. A005730, A005731.

Sequence in context: A200563 A284577 A122018 * A271504 A086660 A271503

Adjacent sequences:  A005726 A005727 A005728 * A005730 A005731 A005732

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Emeric Deutsch, Jan 24 2005

New name from Michel Marcus, Apr 27 2016

STATUS

approved

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Last modified February 17 10:59 EST 2019. Contains 320219 sequences. (Running on oeis4.)