A088075 Smallest number sandwiched between two numbers having exactly n prime divisors.

3, 11, 131, 1429, 77141, 1456729, 117048931, 10326137821, 1110819807371, 140734085123059, 11639258217451019

Offset

1,1

Comments

a(n)=m is the smallest number sandwiched between m-1 and m+1 such that both m+1 and m-1 have n distinct prime-factors. No restrictions are imposed for {m-1,m+1} flanker numbers.

References

Jean-Marie De Koninck, "Those Fascinating Numbers", American Mathematical Society, 2009, entry 1428. (This gives the lower of the two numbers.)

Links

Table of n, a(n) for n=1..11.

Formula

a(n) = Min{A001221(x-1) = A001221(x+1) = n} x.

Example

n = 3: a(3) = 131, 130 = 2*5*13 and 132 = 2^2*3*11 both have three prime divisors.
n = 6: a(6) = 1456729 = 103*14143 is between 1456728 = 8*3*7*13*23*29 and 1456730 = 2*5*11*17*19*41.

Prog

(PARI) isok(k, n) = (omega(k-1)==n) && (omega(k+1)==n);
a(n) = my(k=2); while (!isok(k, n), k++); k; \\ Michel Marcus, Sep 03 2023

Crossrefs

Cf. A088076, A088077, A001221.

Sequence in context: A274664 A219620 A201611 * A088076 A375792 A276258

Adjacent sequences: A088072 A088073 A088074 * A088076 A088077 A088078

Keyword

nonn,more

Author

Amarnath Murthy, Sep 22 2003

Extensions

Edited by Labos Elemer, Sep 30 2003

More terms from Ray Chandler, Oct 07 2003

a(8)-a(9) from Donovan Johnson, Jun 19 2008

a(10)-a(11) from Donovan Johnson, Feb 18 2009

Status

approved