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A370635 a(n) is the index m of the smallest term k = A135507(m) such that prime(n) | k.

%I A370635 #17 May 19 2024 13:16:08
%S A370635 2,4,3,47,53,11,83,17,67,317,29,257,367,41,233,157,293,59,467,211,71,
%T A370635 709,911,443,677,503,101,2459,107,337,379,653,409,137,743,149,1097,
%U A370635 487,499,863,2683,179,953,191,983,197,631,1559,6581,227,1163,1193,239,751
%N A370635 a(n) is the index m of the smallest term k = A135507(m) such that prime(n) | k.
%H A370635 Michael De Vlieger, <a href="/A370635/b370635.txt">Table of n, a(n) for n = 1..2074</a> (terms a(n) <= 2^20.)
%F A370635 a(n) > n for all n; a(n) >= prime(a(n)) - 2 for n > 1.
%e A370635 Let b(x) = A135507(x) and c(x) = A370634(x).
%e A370635 a(1) = 2 since prime(1) | b(2), i.e., 2 | 4. Also 2 | c(2), where c(2) = 4.
%e A370635 a(2) = 4 since prime(2) | b(4), i.e., 3 | 60. Also 3 | c(4), where c(4) = 3.
%e A370635 a(3) = 3 since prime(3) | b(3), i.e., 5 | 20. Also 5 | c(3), where c(3) = 5.
%e A370635 a(4) = 47 since prime(4) | a(47), where a(47) = 2^6 * 3^37 * 5^5 * 7^2 * 13^5 * 19^2 * 31 * 43. Also, 7 | c(47), where c(47) = 49, etc.
%t A370635 nn = 10^4; c[_] := 0; j = 1;
%t A370635 {1}~Join~Monitor[Do[k = 2 j + LCM[j, i];
%t A370635    Map[If[c[#] == 0, Set[c[#], i]] &, FactorInteger[k/j][[All, 1]] ];
%t A370635    j = k, {i, 2, nn}], i];
%t A370635 TakeWhile[Array[c[Prime[#]] &, PrimePi[nn + 2]], # > 0 &]
%Y A370635 Cf. A135507, A370634.
%K A370635 nonn
%O A370635 1,1
%A A370635 _Michael De Vlieger_, May 19 2024