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A322354 Greatest common divisor of product p and product (p+2), where p ranges over distinct prime divisors of n; a(n) = gcd(A007947(n), A166590(A007947(n))). 4
1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 5, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 1, 2, 1, 10, 1, 2, 1, 2, 7, 2, 1, 2, 3, 2, 1, 6, 1, 2, 5, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 1, 10, 1, 2, 3, 2, 5, 2, 1, 2, 1, 14, 1, 2, 1, 2, 5, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 10, 1, 2, 3, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 105 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..15015

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

FORMULA

a(n) = A322362(A007947(n)) = gcd(A007947(n), A166590(A007947(n))).

a(n) = A322356(n) * A322357(n).

MATHEMATICA

f[n_] := If[n == 1, 1, Times @@ Power @@@ ({#[[1]] + 2, #[[2]]} & /@ FactorInteger[n])]; rad[n_] := Times @@ (First@# & /@ FactorInteger@n); a[n_] := GCD[rad[n], f[rad[n]]]; Array[a, 120] (* Amiram Eldar, Dec 16 2018 *)

PROG

(PARI)

A166590(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] += 2); factorback(f); };

A322362(n) = gcd(n, A166590(n));

A007947(n) = factorback(factorint(n)[, 1]);

A322354(n) = A322362(A007947(n));

\\ Alternatively as:

A322354(n) = gcd(A007947(n), A166590(A007947(n)));

CROSSREFS

Cf. A007947, A166590, A322356, A322357, A322362.

Cf. also A066086.

Sequence in context: A161304 A161279 A160983 * A336312 A161237 A161061

Adjacent sequences:  A322351 A322352 A322353 * A322355 A322356 A322357

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 16 2018

STATUS

approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)