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 A298155 For any n >= 0 and k > 0, the prime(k)-adic valuation of a(n) equals the prime(k)-adic valuation of n + k (where prime(k) denotes the k-th prime). 2
 1, 6, 5, 28, 3, 2, 11, 4680, 1, 2, 357, 76, 5, 6, 23, 16, 9, 770, 1, 348, 403, 2, 75, 8, 7, 1998, 1, 340, 1353, 86, 19, 672, 235, 26, 9, 4, 1, 36570, 7, 88, 3, 2, 295, 2196, 17, 98, 39, 400, 1943, 114, 11, 8804, 68985, 2, 1, 24, 1, 790, 3, 364, 1909, 3366, 185 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This sequence has similarities with A102370: here, for k > 0, a(n) and n + k have the same prime(k)-adic valuation, there, for k >= 0, A102370(n) and n + k have the same k-th binary digit (the least significant binary digit having index 0). For any positive number, say k, we can use the Chinese remainder theorem to find a term that is a multiple of k; this term has index < k. a(n) is even iff n is odd. See A298161 for the indices of ones in the sequence. LINKS Rémy Sigrist, Table of n, a(n) for n = 0..10000 FORMULA For any n >= 0: - a(n) = Product_{ k > 0 } A000040(k)^A060175(n + k, k) (this product is well defined as only finitely many terms are > 1), - A007814(a(n)) = A007814(n + 1), - A007949(a(n)) = A007949(n + 2), - A112765(a(n)) = A112765(n + 3), - A214411(a(n)) = A214411(n + 4), - gcd(n, a(n)) = 1. For any n > 0: - a(A073605(n)) is a multiple of A002110(n). EXAMPLE For n = 7: - the 2-adic valuation of 7 + 1 is 3, - the 3-adic valuation of 7 + 2 is 2, - the 5-adic valuation of 7 + 3 is 1, - the 7-adic valuation of 7 + 4 is 0, - the 11-adic valuation of 7 + 5 is 0, - the 13-adic valuation of 7 + 6 is 1, - for k > 6, the prime(k)-adic valuation of 7 + k is 0, - hence a(7) = 2^3 * 3^2 * 5^1 * 13^1 = 4680. MAPLE f:= proc(n) local v, p, k;   v:= 1: p:= 1:   for k from 1 do     p:= nextprime(p);     if p > n+k then return v fi;     v:= v * p^padic:-ordp(n+k, p)   od end proc: map(f, [\$0..100]); # Robert Israel, Jan 16 2018 MATHEMATICA f[n_] := Module[{v = 1, p = 1, k}, For[k = 1, True, k++, p = NextPrime[p]; If[p > n + k, Return[v]]; v *= p^IntegerExponent[n + k, p]]]; f /@ Range[0, 100] (* Jean-François Alcover, Jul 30 2020, after Maple *) PROG (PARI) a(n) = my (v=1, k=0); forprime(p=1, oo, k++; if (n+k < p, break); v *= p^valuation(n+k, p)); return (v) CROSSREFS Cf. A000040, A002110, A007814, A007949, A060175, A073605, A102370, A112765, A214411, A298161. Sequence in context: A228969 A256961 A267743 * A219931 A296192 A070399 Adjacent sequences:  A298152 A298153 A298154 * A298156 A298157 A298158 KEYWORD nonn AUTHOR Rémy Sigrist, Jan 13 2018 STATUS approved

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Last modified October 27 19:53 EDT 2021. Contains 348288 sequences. (Running on oeis4.)