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A093550 a(n) is the smallest number m such that each of the numbers m-1, m and m+1 is a product of n distinct primes. 12
34, 1310, 203434, 16467034, 1990586014, 41704979954, 102099792179230, 22192526378762466 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

Each term of this sequence is of the form 4k+2.

LINKS

Table of n, a(n) for n=2..9.

Jacques Tramu, Puzzle 371

EXAMPLE

a(5)=16467034 because each of the three numbers 16467034-1, 16467034 & 16467034+1 are products of 5 distinct primes (16467033=3*11*17*149*197, 16467034=2*19*23*83*227, 16467035=5*13*37*41*167) and 16467034 is the smallest such number.

MATHEMATICA

a[n_] := a[n] = (For[m=1, !(Length[FactorInteger[4m+1]]==n && SquareFreeQ[4m+1] && Length[FactorInteger[4m+2]]==n && SquareFreeQ[4m+2] && Length[FactorInteger[4m+3]]==n && SquareFreeQ[4m+3]), m++ ]; 4m+2); Table[Print[a[n]]; a[n], {n, 2, 6}] (* updated by Jean-François Alcover, Jul 04 2013 *)

PROG

(PARI) a(n)={my(m=1); while(!(issquarefree(m-1)&&issquarefree(m)&&issquarefree(m+1)&&omega(m-1)==n&&omega(m)==n&&omega(m+1)==n), m++); return(m); } main(size)={my(n); return(vector(size, n, a(n+1))); } /* Anders Hellström, Jul 14 2015 */

CROSSREFS

Cf. A093549, A052215, A093548, A248201, A248202, A248203, A248204, A259349, A259350, A259801.

Sequence in context: A251924 A158731 A297693 * A296587 A212735 A123790

Adjacent sequences:  A093547 A093548 A093549 * A093551 A093552 A093553

KEYWORD

more,nonn

AUTHOR

Farideh Firoozbakht, Apr 07 2004, corrected Aug 26 2006

EXTENSIONS

a(7) added from Jacques Tramu's web site by Farideh Firoozbakht, Aug 26 2006

a(8) from Donovan Johnson, Oct 27 2008

a(9) from James G. Merickel, Jul 24 2015

STATUS

approved

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Last modified April 18 10:56 EDT 2021. Contains 343087 sequences. (Running on oeis4.)