A093548
a(n) is the smallest number m such that each of the numbers m and m+1 has n distinct prime divisors.
Original entry on oeis.org
2, 14, 230, 7314, 254540, 11243154, 965009045, 65893166030, 5702759516090, 490005293940084, 76622240600506314
Offset: 1
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
- J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 230, p. 65, Ellipses, Paris 2008.
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a[n_] := (For[m=1, !(Length[FactorInteger[m]]==n && Length[FactorInteger[m+1]]==n), m++ ];m);Do[Print[a[n]], {n, 7}]
Flatten[Table[SequencePosition[PrimeNu[Range[260000]],{n,n},1],{n,5}],1][[;;,1]] (* To generate more terms, increase the Range and n constants. *) (* Harvey P. Dale, Jun 08 2023 *)
-
from sympy import primefactors, primorial
def a(n):
m = primorial(n)
while True:
if len(primefactors(m)) == n:
if len(primefactors(m+1)) == n: return m
else: m += 2
else: m += 1
for n in range(1, 6):
print(a(n), end=", ") # Michael S. Branicky, Feb 14 2021
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.
Original entry on oeis.org
34, 1310, 203434, 16467034, 1990586014, 41704979954, 102099792179230, 22192526378762466
Offset: 2
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.
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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 *)
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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 */
A052215
a(n) = smallest number m such that m and m+1 are the product of exactly n distinct primes.
Original entry on oeis.org
2, 14, 230, 7314, 378014, 11243154, 965009045, 65893166030, 5702759516090, 605247139068494, 78971815814237709, 22593106657425552170
Offset: 1
14 and 15 are both the product of 2 primes.
230 is the 3rd entry because we have (230=2*5*23, 231=3*7*11).
A113752
Smallest number m such that m, m+1 and m+2 have exactly n prime factors (counted with multiplicity).
Original entry on oeis.org
33, 170, 1274, 15470, 33614, 3145310, 40909374, 668363967, 9864741248, 179199427328, 967461818750, 57938945781248, 597779386906624
Offset: 2
a(6) = 33614 = 2*7*7*7*7*7, a(6)+1 = 3*3*3*3*5*83, a(6)+2 = 2*2*2*2*11*191
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t = {}; n = 2; m = 1; While[Length[t] < 5, m++; If[n == PrimeOmega[m] == PrimeOmega[m + 1] == PrimeOmega[m + 2], AppendTo[t, m]; n++]]; t (* T. D. Noe, Aug 19 2013 *)
Showing 1-4 of 4 results.
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