A370635 a(n) is the index m of the smallest term k = A135507(m) such that prime(n) | k.
2, 4, 3, 47, 53, 11, 83, 17, 67, 317, 29, 257, 367, 41, 233, 157, 293, 59, 467, 211, 71, 709, 911, 443, 677, 503, 101, 2459, 107, 337, 379, 653, 409, 137, 743, 149, 1097, 487, 499, 863, 2683, 179, 953, 191, 983, 197, 631, 1559, 6581, 227, 1163, 1193, 239, 751
Offset: 1
Keywords
Examples
Let b(x) = A135507(x) and c(x) = A370634(x). a(1) = 2 since prime(1) | b(2), i.e., 2 | 4. Also 2 | c(2), where c(2) = 4. a(2) = 4 since prime(2) | b(4), i.e., 3 | 60. Also 3 | c(4), where c(4) = 3. a(3) = 3 since prime(3) | b(3), i.e., 5 | 20. Also 5 | c(3), where c(3) = 5. 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.
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..2074 (terms a(n) <= 2^20.)
Programs
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Mathematica
nn = 10^4; c[_] := 0; j = 1; {1}~Join~Monitor[Do[k = 2 j + LCM[j, i]; Map[If[c[#] == 0, Set[c[#], i]] &, FactorInteger[k/j][[All, 1]] ]; j = k, {i, 2, nn}], i]; TakeWhile[Array[c[Prime[#]] &, PrimePi[nn + 2]], # > 0 &]
Formula
a(n) > n for all n; a(n) >= prime(a(n)) - 2 for n > 1.