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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

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 21 06:25 EDT 2018. Contains 316405 sequences. (Running on oeis4.)