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A093548 a(n) is the smallest number m such that each of the numbers m and m+1 has n distinct prime divisors. 10
2, 14, 230, 7314, 254540, 11243154, 965009045, 65893166030, 5702759516090, 490005293940084, 76622240600506314 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Prime factors may be repeated in m and m+1. The difference between this sequence and A052215 is that in the latter, no prime factor may be repeated. So A052215 imposes more stringent conditions, hence a(n) <= A052215(n). - N. J. A. Sloane, Nov 21 2015

2^63 < a(12) <= 22593106657425552170. - Donovan Johnson, Jan 08 2009

A115186(n) <= a(n) <= A052215(n). - Zak Seidov, Jan 16 2015

REFERENCES

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 230, p. 65, Ellipses, Paris 2008.

LINKS

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

FORMULA

a[n_] := (For[m=1, !(Length[FactorInteger[m]]==n && Length[FactorInteger[m+1]]==n), m++ ];m)

EXAMPLE

a(5) = 254540 because 254540=2^2*5*11*13*89; 254541=3*7*17*23*31

and 254540 is the smallest number m which each of the numbers m & m+1 has 5 distinct prime divisors.

In contrast, A052215(5) = 378014 > 254540. - N. J. A. Sloane, Nov 21 2015

MATHEMATICA

a[n_] := (For[m=1, !(Length[FactorInteger[m]]==n && Length[FactorInteger[m+1]]==n), m++ ]; m); Do[Print[a[n]], {n, 7}]

CROSSREFS

Cf. A052215 (another version), A093549, A093550, A115186.

Sequence in context: A251692 A118086 A048163 * A052215 A053846 A053855

Adjacent sequences:  A093545 A093546 A093547 * A093549 A093550 A093551

KEYWORD

nonn,more

AUTHOR

Farideh Firoozbakht, Apr 06 2004

EXTENSIONS

a(8), a(9) from Martin Fuller, Jan 17 2006

a(10)-a(11) from Donovan Johnson, Jan 08 2009

STATUS

approved

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Last modified January 17 19:58 EST 2019. Contains 319251 sequences. (Running on oeis4.)