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 A322370 For any n > 4: let p be the n-th prime number; a(n) is the least squarefree p-smooth integer congruent to 4 modulo p. 1
 15, 30, 21, 42, 119, 33, 35, 78, 209, 133, 51, 57, 299, 65, 138, 217, 77, 399, 87, 93, 295, 105, 210, 111, 222, 230, 258, 266, 141, 143, 451, 155, 161, 330, 505, 177, 183, 185, 195, 390, 201, 203, 215, 1342, 231, 462, 237, 721, 1209, 255, 518, 267, 273, 546 (list; graph; refs; listen; history; text; internal format)
 OFFSET 5,1 COMMENTS This sequence is well-defined per the work of Booker and Pomerance. The number 4 in the congruence in the name could be replaced by any value; this number was chosen for being the first integer that is not squarefree. LINKS Rémy Sigrist, Table of n, a(n) for n = 5..10000 Andrew R. Booker, Carl Pomerance, Squarefree smooth numbers and Euclidean prime generators, arXiv:1607.01557 [math.NT], 2016-2017. Andrew R. Booker and Carl Pomerance, Squarefree smooth numbers and Euclidean prime generators, Proceedings of the American Mathematical Society 145 (2017), 5035-5042. Rémy Sigrist, Colored scatterplot of (n, a(n)) for n = 5..1000000 (where the color is function of (a(n)-4)/A000040(n)). FORMULA a(n) = A261144(n, k) for some k in 1..2^n. EXAMPLE For n = 7: - the 7th prime is 17, - the first squarefree 17-smooth integers s, alongside (s-4) mod 17, are: s 1 2 3 5 6 7 10 11 13 14 15 17 21 ------------ -- -- -- - - - -- -- -- -- -- -- -- (s-4) mod 17 14 15 16 1 2 3 6 7 9 10 11 13 0 - hence a(7) = 21. MATHEMATICA a[n_] := Module[{p = Prime[n], k = 4}, While[! SquareFreeQ[k] || FactorInteger[k][[-1, 1]] > p, k += p; Continue[]]; k]; Array[a, 100, 5] (* Amiram Eldar, Dec 08 2018 *) PROG (PARI) a(n) = my (p=prime(n)); forstep (v=4, oo, p, if (issquarefree(v), my (f=factor(v)); if (f[#f~, 1] <= p, return (v)))) CROSSREFS Cf. A000040, A005117, A261144. Sequence in context: A196184 A201136 A200896 * A040210 A296758 A297285 Adjacent sequences: A322367 A322368 A322369 * A322371 A322372 A322373 KEYWORD nonn AUTHOR Rémy Sigrist, Dec 05 2018 STATUS approved

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Last modified November 30 21:14 EST 2023. Contains 367462 sequences. (Running on oeis4.)