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A294906 a(n) is the least squarefree integer, product of n primes that are symmetrically distributed around their average. 0
2, 6, 105, 2145, 53295, 1616615, 57998985, 3038795305, 3907126810041, 7292509103495, 66240019730740785, 82246340873964085, 1870667082297874652055, 343515424581301546805, 9160656702012692171113335, 2356596317899272514936585, 1903895854998638367242867256645 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..17.

EXAMPLE

The prime factors of the first terms are: [2], [2, 3], [3, 5, 7], [3, 5, 11, 13], [3, 5, 11, 17, 19], [5, 7, 11, 13, 17, 19], [3, 5, 11, 17, 23, 29, 31], ...

MAPLE

with(numtheory): P:=proc(q) local a, b, j, k, n, p, t, ok; p:=2; t:=2; print(2);

for n from 2 to q do p:=nextprime(p); t:=t*p; for j from t to q do if not isprime(j) and issqrfree(j) then a:=ifactors(j)[2]; if nops(a)=n then b:=2*add(a[k][1], k=1..nops(a))/nops(a); ok:=1;

for k from 1 to trunc(nops(a)/2) do if a[k][1]+a[nops(a)-k+1][1]<>b then ok:=0; break; fi; od; if ok=1 then print(j); break; fi; fi; fi; od; od; end: P(10^9); # Paolo P. Lava, Nov 10 2017

PROG

(PARI) isok(n, nb) = {if (issquarefree(n) && (omega(n)==nb), f = factor(n)[, 1]~; avg = vecsum(f)/#f; for (k=1, #f\2, if (f[k] + f[#f-k+1] != 2*avg, return(0)); ); return (1); ); }

a(n) = {my(k = prod(i=1, n, prime(i))); while (! isok(k, n), k++); k; }

CROSSREFS

Cf. A262723, A294751, A294752, A294776.

Sequence in context: A054247 A278888 A099790 * A284262 A287935 A181036

Adjacent sequences:  A294903 A294904 A294905 * A294907 A294908 A294909

KEYWORD

nonn

AUTHOR

Michel Marcus, Nov 10 2017

EXTENSIONS

a(8)-a(17) from Giovanni Resta, Nov 10 2017

STATUS

approved

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Last modified August 8 02:45 EDT 2020. Contains 336290 sequences. (Running on oeis4.)