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A048942 a(n) is twice the coefficient of the radical part in the fundamental unit of Q(sqrt(A000037(n))) where A000037 lists the nonsquare numbers. 1
2, 2, 1, 4, 6, 2, 2, 6, 2, 1, 8, 2, 2, 2, 78, 1, 1, 84, 10, 4, 2, 2, 6, 1, 4, 546, 2, 8, 12, 2, 2, 12, 8, 2, 10, 4, 1062, 6, 1, 7176, 14, 2, 2, 14, 1, 1, 4, 24, 8, 40, 26, 138, 2, 5, 16, 6, 2, 16, 11934, 2, 3, 60, 826, 2, 250, 10, 2, 78, 1, 12, 18, 1, 2, 18, 1, 1, 2244, 6, 84 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The radical part is actually sqrt(A007913(A000037(n))) where A007913(m) is the squarefree part of m. - Michel Marcus, Jun 26 2020

LINKS

Table of n, a(n) for n=1..79.

S. R. Finch, Class number theory

Steven R. Finch, Class number theory [Cached copy, with permission of the author]

Eric Weisstein's World of Mathematics, Fundamental Unit.

PROG

(PARI) a(n) = {if (issquare(n), return (0)); if (!issquarefree(n), m = core(n), m = n); my(u = abs(2*polcoeff(lift(bnfinit(x^2-m, 1).fu[1]), 0))); if (u^2==1, return (1)); if (u^2==4, return (sqrtint((u^2+4)/m)); ); if (u^2 < 4, return((u^2+4)/n)); my(v2 = [(u^2-4)/m, (u^2+4)/m]); sqrtint(vecmin(select(x->denominator(x)==1, v2))); } \\ Michel Marcus, Jun 25 2020

CROSSREFS

Cf. A000037, A007913, A048941.

Sequence in context: A115313 A121484 A273903 * A080928 A068957 A119468

Adjacent sequences:  A048939 A048940 A048941 * A048943 A048944 A048945

KEYWORD

nonn

AUTHOR

Eric W. Weisstein

EXTENSIONS

Name edited and some terms corrected by Michel Marcus, Jun 26 2020

STATUS

approved

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Last modified May 16 22:18 EDT 2021. Contains 343957 sequences. (Running on oeis4.)