Sample extra PARI program output (when prt is set to allow it) for a(3), a(4), ..., a(31). L := L(n) := LCM(1,2,...,n); k := k(n), where 1 <= k <= n!/L, is the multiplier of the LCM for a(n), i.e., a(n) = k*L. n = 3: k*L = 1*6 = 6 = 2*3 = 3!/1! n = 4: k*L = 1*12 = 12 = 3*4 = 4!/2! n = 5: k*L = 1*60 = 60 = 3*4*5 = 5!/2! n = 6: k*L = 1*60 = 60 = 3*4*5 = 5!/2! n = 7: k*L = 1*420 = 420 = 20*21 = 21!/19! n = 8: k*L = 1*840 = 840 = 4*...*7 = 7!/3! n = 9: k*L = 1*2520 = 2520 = 3*...*7 = 7!/2! n = 10: k*L = 1*2520 = 2520 = 3*...*7 = 7!/2! n = 11: k*L = 2*27720 = 55440 = 7*...*11 = 11!/6! n = 12: k*L = 2*27720 = 55440 = 7*...*11 = 11!/6! n = 13: k*L = 1*360360 = 360360 = 11*...*15 = 15!/10! n = 14: k*L = 1*360360 = 360360 = 11*...*15 = 15!/10! n = 15: k*L = 1*360360 = 360360 = 11*...*15 = 15!/10! n = 16: k*L = 3*720720 = 2162160 = 9*...*14 = 14!/8! n = 17: k*L = 7*12252240 = 85765680 = 440*441*442 = 442!/439! n = 18: k*L = 7*12252240 = 85765680 = 440*441*442 = 442!/439! n = 19: k*L = 144*232792560 = 33522128640 = 11*...*19 = 19!/10! n = 20: k*L = 144*232792560 = 33522128640 = 11*...*19 = 19!/10! n = 21: k*L = 144*232792560 = 33522128640 = 11*...*19 = 19!/10! n = 22: k*L = 144*232792560 = 33522128640 = 11*...*19 = 19!/10! n = 23: k*L = 3600*5354228880 = 19275223968000 = 17*...*26 = 26!/16! n = 24: k*L = 3600*5354228880 = 19275223968000 = 17*...*26 = 26!/16! n = 25: k*L = 720*26771144400 = 19275223968000 = 17*...*26 = 26!/16! n = 26: k*L = 720*26771144400 = 19275223968000 = 17*...*26 = 26!/16! n = 27: k*L = 240*80313433200 = 19275223968000 = 17*...*26 = 26!/16! n = 28: k*L = 240*80313433200 = 19275223968000 = 17*...*26 = 26!/16! n = 29: k*L = 15576*2329089562800 = 36277899030172800 = 114*...*121 = 121!/113! n = 30: k*L = 15576*2329089562800 = 36277899030172800 = 114*...*121 = 121!/113! n = 31: k*L = 512238*72201776446800 = 36984493563555938400 = 6081487775*6081487776 = 6081487776!/6081487774! Notes: Calculation of a(31), an oblong number, required about 45 hours (and was run with PARI default memory allocation quadrupled). To prevent running this program unnecessarily, observe that if LCM(1,...,m) = LCM(1,...,n), then a(m) = a(n). For example, a(n) = a(32) -- and the output would be identical -- for n = 33, ..., 36, as all five LCMs are 144403552893600. (The converse is not true, i.e., a(m) = a(n) does not imply that LCM(1,...,m) = LCM(1,...,n). For this example, see the line above for a(24), where k*L = 3600*5354228880, and for a(25), where k*L = 720*26771144400. Another example is seen when comparing a(26) and a(27).) But is a(32) = a(31) also? Yes: Although the respective LCMs are 144403552893600 and 72201776446800, the former is twice the latter. Thus, as a(31) is being calculated by looking at k*72201776446800 with k running from 1 to 512238, all multiples k'*144403552893600 are simultaneously being checked with k' running from 1 to 512238/2. This means that a(32) = (512238/2)*144403552893600, so we know without running a(32) that its output must be k*L = 256119*144403552893600 = 36984493563555938400 = 6081487775*6081487776 = 6081487776!/6081487774! In general, if L(n+1)/L(n) = j and k(n)/j is an integer, then a(n+1) = a(n). This situation is entirely similar to the above results already seen with a(24), a(25), a(26), and a(27). By the earlier remarks, then the terms and output lines for a(33) through a(36) are also the same as a(32)'s.