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 A253769 #24 Jul 12 2025 12:30:45
%S A253769 3,5,10,16,29,37,52,60,76,103,113,142,160,170,188,219,249,263,294,314,
%T A253769 328,358,379,413,461,484,494,516,530,554,637,659,697,707,768,782,822,
%U A253769 858,878,919,953,973,1033,1049,1072,1086,1168,1240,1267,1281,1307,1343,1365,1423,1468,1504,1544,1562,1604,1632,1642,1709
%N A253769 Sum of number of divisors of all positive integers <= prime(n).
%C A253769 a(n) is the index of the first position of prime(n) in A027750, the sequence that lists the divisors of all integers. - _Michel Marcus_, Oct 17 2015
%H A253769 Chai Wah Wu, <a href="/A253769/b253769.txt">Table of n, a(n) for n = 1..10000</a>
%F A253769 a(n) = A006218(A000040(n)).
%e A253769 For n = 3 the third prime number is 5 and the sum of the number of divisors of the first five positive integers is 1 + 2 + 2 + 3 + 2 = 10, so a(3) = 10.
%t A253769 Module[{nn=300,d},d=Accumulate[DivisorSigma[0,Range[nn]]];Table[d[[k]],{k,Prime[Range[PrimePi[nn]]]}]] (* _Harvey P. Dale_, Jul 12 2025 *)
%o A253769 (PARI) a(n) = sum(i=1, prime(n), numdiv(i)); \\ _Michel Marcus_, Jan 15 2015
%o A253769 (Python)
%o A253769 from math import isqrt
%o A253769 from sympy import prime
%o A253769 def A253769(n): return (lambda m, p: 2*sum(p//k for k in range(1, m+1))-m*m)(isqrt(prime(n)),prime(n)) # _Chai Wah Wu_, Oct 09 2021
%Y A253769 Cf. A000005, A000040, A006218, A027750, A244576, A244578, A244583.
%Y A253769 Partial sums of A139140.
%K A253769 nonn
%O A253769 1,1
%A A253769 _Omar E. Pol_, Jan 14 2015