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 A366048 #13 Sep 27 2023 13:45:36 %S A366048 1,2,1,25,54,7,53,65,6,22,51,49,343,209,416,624,17,18,338,410,1622, %T A366048 341,140,849,139,337,1939,338,849,4365,2565,6368,496,4366,132,8392, %U A366048 131,4453,128,4173,127,487,123,4437,492,122,3011,491,3724,4171,2637,1231,1631,12765,119 %N A366048 For n >= 1, a(n) is the least k >= 1 such that 1/d(k) + … + 1/d(k + n - 1) is an integer, d(i) = A000005(i). %C A366048 Conjecture : The sum 1/d(k) + … + 1/d(k + n - 1) = C, C an integer, exists for all k >= 1, n >= 1. %C A366048 Are there, for some fixed n >= 3, infinitely many k's such that 1/d(k) + … + 1/d(k + n - 1) is an integer ? %e A366048 n = 3: 1/d(k) + 1/d(k + 1) + 1/d(k + 2) = C, C an integer, is valid for the least k = 1, thus a(3) = 1. %e A366048 n = 4: 1/d(k) + 1/d(k + 1) + 1/d(k + 2) + 1/d(k + 3) = C, C an integer, is valid for the least k = 25, thus a(4) = 25. %o A366048 (PARI) a(n) = my(k=1); while (denominator(sum(i=0, n-1, 1/numdiv(k+i))) != 1, k++); k; \\ _Michel Marcus_, Sep 27 2023 %Y A366048 Cf. A000005, A359056. %K A366048 nonn %O A366048 1,2 %A A366048 _Ctibor O. Zizka_, Sep 27 2023 %E A366048 More terms from _Michel Marcus_, Sep 27 2023