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A246463 a(n) = min(p +- q) > 1 with p*q being equal to the n-th primorial (A002110). 0
5, 7, 11, 13, 17, 107, 41, 157, 1811, 1579, 18859, 95533, 17659, 1995293, 208303, 2396687, 58513111, 299808329, 3952306763, 341777053, 115405393057, 437621467859, 1009861675153, 6660853109087, 29075165225531, 418895584426457, 2371362636817019, 6889206780487667, 5258351738694673 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

All terms must be odd since 2 is only represented once in the factorization of any primorial. The two divisors of different parity, p and q, must straddle the square root of the primorial.

LINKS

Table of n, a(n) for n=2..30.

EXAMPLE

a(7) = 41 since the middle four divisors of 7# or 2*3*5*7*11*13*17 = 510510 are 663, 714, 715 and 770. Because the middle two only differ by 1, the next pair, 663 and 770 are used and their difference is 107.

a(8) = 41 since the middle two divisors of 8# are 3094 and 3135 which have a difference of 41.

MATHEMATICA

f[n_] := Block[{k = mx = 1, fi = Prime@ Range@ n, prod = Fold[Times, 1, Prime@ Range@ n], sqrt, tms}, sqrt = Floor@ Sqrt@ prod; While[k < 2^n, tms = Times @@ (fi^IntegerDigits[k, 2, n]); If[mx < tms < sqrt, mx = tms]; k++]; prod/mx - mx]; Array[f, 30, 2]

PROG

(PARI) a(n)=my(P=prod(i=1, n, prime(i))); forstep(k=sqrtint(P), 1, -1, if(P%k==0 && P/k-k>1, return(P/k-k))) \\ Charles R Greathouse IV, Aug 31 2014

(PARI) a(n)=my(P=prod(i=1, n, prime(i)), t); fordiv(P, d, if(P/d-d>1, t=P/d-d, return(t))) \\ Charles R Greathouse IV, Aug 31 2014

CROSSREFS

Cf. A003681, A002110.

Sequence in context: A007529 A287956 A266266 * A314297 A108409 A291345

Adjacent sequences:  A246460 A246461 A246462 * A246464 A246465 A246466

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Aug 26 2014

STATUS

approved

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Last modified October 17 16:34 EDT 2018. Contains 316285 sequences. (Running on oeis4.)