This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A075036 #102 Nov 09 2023 08:52:33 %S A075036 2,14,44,104,2511,735,29888,2295,6075,5264,2200933376,5984,689278976, %T A075036 156735,180224,21735,2035980763136,223244,9399153082499072,458864, %U A075036 41680575,701443071,2503092614937444351,201824,2707370000,29785673727,46977524,5475519,1737797404898095794225152 %N A075036 Smaller of two smallest consecutive numbers with 2n divisors. %C A075036 There cannot be two consecutive numbers with the same odd number of divisors as both cannot be squares. %C A075036 These numbers have the property that a(n) * (a(n) + 1) has 4*n^2 divisors. - _David A. Corneth_, Jun 24 2016 %C A075036 Conjecture: if a term k is even, the highest p-adic order of k (the maximum may be attained by several p's) occurs at p=2 and the highest p-adic order of k+1 occurs at p=3. If a term k is odd, the highest p-adic order of k occurs at p=3 and the highest p-adic order of k+1 occurs at p=2. - _Chai Wah Wu_, Mar 12 2019 %C A075036 a(49) = 378401464109375, a(58) = 79921490583489592950783. - _Jon E. Schoenfield_, May 07 2022 %C A075036 a(51) = 34210814718574592, a(55) = 2481402804069375, a(57) = 394311388855795712. - _Jon E. Schoenfield_, Nov 06 2023 - Nov 08 2023 %H A075036 Chai Wah Wu, <a href="/A075036/b075036.txt">Table of n, a(n) for n = 1..48</a> %H A075036 Ray Chandler, <a href="/A075036/a075036_10.txt">Known terms and upper limits</a>. %F A075036 a(n) <= A215199(n-1) for n > 1. Conjecture: if p is prime, then a(p) = A215199(p-1). This conjecture is true if the conjecture in A215199 is true. The b-file of A215199 thus shows that a(p) = A215199(p-1) for prime p < 1279. - _Chai Wah Wu_, Mar 12 2019 %e A075036 a(4) = 104 as tau(104) = tau(105) = 8. %t A075036 a[n_] := (For[k=1, ! (DivisorSigma[0, k] == 2*n && DivisorSigma[0, k+1] == 2*n), k++]; k); Array[a, 10] (* _Giovanni Resta_, Jun 24 2016 *) %o A075036 (PARI) a(n) = my(k=1); while(numdiv(k)!=2*n || numdiv(k+1)!=2*n, k++); k \\ _Felix Fröhlich_, Jun 24 2016 %Y A075036 Cf. A000005, A005237, A039832, A049103, A174456, A215197, A215199, A274357, A274358, A274359. %K A075036 nonn %O A075036 1,1 %A A075036 _Amarnath Murthy_, Sep 03 2002 %E A075036 a(5)-a(24) from _Max Alekseyev_, Mar 12 2009 %E A075036 a(25)-a(28) from _Giovanni Resta_, Jun 24 2016 %E A075036 a(29) from _Chai Wah Wu_, Mar 12 2019