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 A077579 #38 May 26 2024 15:58:45
%S A077579 1,3,5,8,15,16,23,48,96,155,208,1956,4245,6816,6907,28515,55568,57765,
%T A077579 203376,437336,746448,963408,1247088,18661696,32187455,113280465,
%U A077579 238564335,368111296,1491581031,1689287568,1831503936,1838097728,2426280688
%N A077579 Numbers k that divide A062273(k).
%C A077579 From _David A. Corneth_, May 25 2024: (Start)
%C A077579 a(n) cannot be equal to 2, 4, 6, 10, 12, 14, 18 (mod 20).
%C A077579 We can ease verification of terms in this sequence by rewriting A062273(k). A062273(k) can be written as blocks of 10 digits followed by some remaining digits like this:
%C A077579 A062273(k) = (B * Sum_{i = 0..(floor(k/10)-1)} (10^10)^i)*10^(k mod 10) + floor(B / (10 ^ (9 - (k-1) mod 10))) = (B * Sum_{i = 0..(floor(k/10)-1)} (10^10)^i)*10^(k mod 10) + floor(B / (10 ^ (9 - (k-1) mod 10))) where B is a block of 10 digits starting with (((k-1)*k)/2 + 1) mod 10 and each successive digit is one more than the previous except after 9 there is 0.
%C A077579 Using modular arithmetic and a simplification for geometric sums we can compute A062273(k) mod k and see if the result is 0.
%C A077579 Also terms are 11670334251, 12057978588, 15925928169. Any missing term must have gcd(t, floor(10^10/9)) > 1. (End)
%H A077579 David A. Corneth, <a href="/A077579/a077579_1.gp.txt">PARI program</a>
%e A077579 From _David A. Corneth_, May 25 2024: (Start)
%e A077579 48 is in the sequence as 48 divides A062273(48). We may write A062273(48) as (9012345678 * Sum_{i = 0..(floor(48)-1)} (10^10)^i)*10^8 + 90123456
%e A077579 = 9012345678 * ((10^10)^4 - 1) / (10^10 - 1) * 10^8 + 90123456
%e A077579 = 1001371742 * ((10^10)^4 - 1) / ((10^10 - 1)/9) * 10^8 + 90123456 and using modular arithmetic (note that (10^10 - 1)/9 is coprime to 48 so we can compute the inverse of the modular class of (10^10 - 1)/9 mod 48. (End)
%o A077579 (PARI) \\ See PARI link
%Y A077579 Cf. A062273, A077577, A077578.
%K A077579 base,nonn,more
%O A077579 1,2
%A A077579 _Amarnath Murthy_, Nov 12 2002
%E A077579 More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 11 2003
%E A077579 Offset corrected and a(12)-a(16) added by _Amiram Eldar_, May 21 2024
%E A077579 a(17)-a(20) from _Michael S. Branicky_, May 22 2024
%E A077579 a(21)-a(23) from _David A. Corneth_ and _Michael S. Branicky_, May 24 2024
%E A077579 a(24)-a(31) from _David A. Corneth_, May 25 2024