A159581
First divisors at which integral quotients occur consecutively in A116536 (and associated with A159580).
Original entry on oeis.org
2747, 6601, 75130, 133386, 148827, 208385, 255445, 799846, 814006, 890299, 993730, 1037571, 1049698, 1382738, 1723170, 1869711, 2168747, 2530165, 2569285, 2615298, 2838135, 2963531, 3020151, 3434151, 3510885, 3627674, 3706710, 3941521, 3999326, 4434411, 4700809, 5887533, 6133305
Offset: 1
The first run of consecutive integers in A051838 is A051838(6)=38 and A051838(7)=39, therefore a(1) = A140763(6)= 2747.
The second run of consecutive integers in A051838 is A051838(13)=56, A051838(14)= 57, A051838(15)=58, therefore a(2) = A140763(13) = 6601.
A159639
Last divisors at which integral quotients occur consecutively.
Original entry on oeis.org
154, 2183, 4002, 8635, 19203, 93017, 96298, 122414, 166762, 182090, 201354, 241237, 337645, 346495, 406813, 456729, 574678, 668811, 781635, 799006, 929442, 952150, 1014194, 1379625, 1455259, 1513549, 1558110, 1573089, 1938354, 2028842
Offset: 1
a(1)=154 because it is the last or second of two divisors (125 being the first) where integral quotients are produced in succession (one after the other): 5577321750/125=44618574, integral; and 161742330750/154=1050274875, integral. See a(4) in A116536, A159578, and A159579.
A266955
Intersection of A046346 (numbers that are divisible by the sum of their prime factors, counted with multiplicity) and A097889 (numbers that are products of at least two consecutive primes).
Original entry on oeis.org
30, 105, 15015, 9699690, 37182145, 215656441, 955049953, 33426748355, 247357937827, 1448810778701, 3710369067405, 304250263527210, 102481630431415235, 1086305282573001491, 261682369333342226303, 37420578814667938361329, 241532826894674874877669
Offset: 1
-
sopfr(n) = {my(f=factor(n)); sum(k=1, #f~, f[k, 1]*f[k, 2]); }
list(lim)= {my(v=List(), p, t); for(e=2, log(lim+.5)\log(2), p=1; t=prod(i=1, e-1, prime(i)); forprime(q=prime(e), lim, t*=q/p; if(t>lim, next(2)); if (! (t % sopfr(t)), listput(v, t)); p=nextprime(p+1))); vecsort(Vec(v));} \\ adapted from A097889
Comments