A097978
a(n) = least m such that m and m+n are both products of exactly n distinct primes.
Original entry on oeis.org
1, 2, 33, 102, 1326, 115005, 31295895, 159282123, 9617162170, 1535531452026, 1960347077019695, 16513791577659519, 271518698440871310
Offset: 0
a(2) = 33 because 33 and 35 are both in A006881.
a(3) = 102 because 102 and 105 are both in A007304.
a(4) = 1326 because 1326 and 1330 are both in A046386.
-
f[n_] := Block[{lst = FactorInteger[n], a, b}, a = Plus @@ Last /@ lst; b = Length[lst]; If[a == b, b, 0]]; g[n_] := Block[{k = Product[ Prime[i], {i, n}]}, While[ f[k] != n || f[k] != f[k + n], k++ ]; k]; Do[ Print[ g[n]], {n, 1, 6}] (* Robert G. Wilson v, Sep 11 2004 *)
Edited and extended by Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 08 2004
A124945
Numbers k such that k and k+10 are 10-almost primes.
Original entry on oeis.org
506240, 789750, 1325312, 1567350, 1761750, 1944800, 2450240, 2579840, 3004928, 3013686, 3093750, 3153654, 3713526, 3844736, 3906240, 4024566, 4394240, 5244416, 5402240, 5431040, 6208640, 6310710, 6932790, 7053750, 7352694, 7585974, 8005878, 8043776, 8099190
Offset: 1
506240=2^7*5*7*113, 506250=2*3^4*5^5;
789750=2*3^5*5^3*13, 789760=2^8*5*617;
1325312=2^8*31*167, 1325322=2*3^8*101;
1567350=2*3^6*5^2*43, 1567360=2^7*5*31*79.
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Select[Range[10^7],PrimeOmega[#]==PrimeOmega[#+10]==10&] (* James C. McMahon, Dec 14 2024 *)
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isok(n) = (bigomega(n) == 10) && (bigomega(n+10) == 10); \\ Michel Marcus, Oct 11 2013
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P=prod(i=1,25,prime(i))^10; v=List(); for(n=1,1e6, g1=gcd(n,P); o1=bigomega(g1); if(o1<5,next); g2=gcd(n+10,P); o2=bigomega(g2); if(o2>=5 && o1+bigomega(n/g1)==10 && o2+bigomega((n+10)/g2)==10, listput(v,n))); Vec(v) \\ Charles R Greathouse IV, Oct 11 2013
A135058
Least m such that both m and m+n have exactly n distinct prime divisors, ignoring multiplicity.
Original entry on oeis.org
1, 2, 10, 102, 1326, 96135, 607614, 159282123, 9617162170, 1110180535035, 28334309296920, 16513791577659519, 271518698440871310
Offset: 0
a(2) = 10 because 10=2*5 and 12=3*2^2 have two distinct prime factors.
a(3) = 102 because 102=2*3*17 and 105=3*5*7 each have three distinct prime factors.
a(5) = 96135 because 96135 = 3*5*13*17*29 and 96140 = 2^2*5*11*19*23 each have 5 distinct prime factors.
A124946
n and n+9 are 9-almost primes.
Original entry on oeis.org
268992, 338976, 516375, 675783, 922176, 984375, 1060695, 1107351, 1164375, 1216215, 1233216, 1361367, 1388736, 1458720, 1668672, 1843632, 1877175, 2018592, 2075463, 2317491, 2333520, 2395575, 2440935, 2457936, 2495367, 2499255, 2546775, 2559375, 2811744
Offset: 1
268992=2^6*3^2*467, 268992+9=269001=3^8*41;
338976=2^5*3^2*11*107, 338976+9=338985=3^7*5*31.
Showing 1-4 of 4 results.
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