A170825 -id:A170825 - cp's OEIS frontend

A181860 a(n) = lcm(n^2, swinging_factorial(n)).

0, 1, 4, 18, 48, 150, 180, 980, 2240, 5670, 6300, 30492, 11088, 156156, 168168, 257400, 1647360, 3719430, 3938220, 17551820, 18475600, 81477396, 85357272, 373173528, 389398464, 1690097500, 1757701400, 7582037400, 3931426800, 33738060600

Offset: 0

Peter Luschny, Nov 21 2010

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Cf. A000290, A056040, A170825, A181861.

A181860 := n -> ilcm(n^2,n!/iquo(n,2)!^2);

Join[{0},sf[n_]:=n!/Quotient[n, 2]!^2; a[n_]:=LCM[n^2, sf[n]]; Table[a[n], {n, 30}] ] (* Jean-François Alcover, Jun 28 2013 *)

a(n) = lcm(n^2, n!/(n\2)!^2); \\ Michel Marcus, Mar 06 2018

a(n) = lcm(A000290(n), A056040(n)).

a(26)-a(29) from Vincenzo Librandi, Mar 05 2018

A343431 Part of n composed of prime factors of the form 6k-1.

Original entry on oeis.org

1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 11, 1, 1, 1, 5, 1, 17, 1, 1, 5, 1, 11, 23, 1, 25, 1, 1, 1, 29, 5, 1, 1, 11, 17, 5, 1, 1, 1, 1, 5, 41, 1, 1, 11, 5, 23, 47, 1, 1, 25, 17, 1, 53, 1, 55, 1, 1, 29, 59, 5, 1, 1, 1, 1, 5, 11, 1, 17, 23, 5, 71, 1, 1, 1, 25, 1, 11, 1, 1, 5, 1, 41, 83, 1, 85, 1, 29, 11, 89, 5

Offset: 1

Peter Munn, Apr 15 2021

Completely multiplicative with a(p) = p if p is of the form 6k-1 and a(p) = 1 otherwise.

Largest term of A259548 that divides n.

Equivalent sequence for distinct prime factors: A170825.
Equivalent sequences for prime factors of other forms: A000265 (2k+1), A343430 (3k-1), A170818 (4k+1), A097706 (4k-1), A248909 (6k+1), A065330 (6k+/-1), A065331 (<= 3), A355582 (<= 5).
Range of terms: A259548.

f[p_, e_] := If[Mod[p, 6] == 5, p^e, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* after Amiram Eldar at A248909 *)

a(n) = {my(f = factor(n)); for (i=1, #f~, if ((f[i, 1] + 1) % 6, f[i, 1] = 1); ); factorback(f); } \\ after Michel Marcus at A248909

from math import prod
from sympy import factorint
def A343431(n): return prod(p**e for p, e in factorint(n).items() if not (p+1)%6) # Chai Wah Wu, Dec 26 2022

a(n) = n / A065331(n) / A248909(n) = A065330(n) / A248909(n).

A170817 a(n) = product of distinct primes of form 4k+1 that divide n.

Original entry on oeis.org

1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 13, 1, 5, 1, 17, 1, 1, 5, 1, 1, 1, 1, 5, 13, 1, 1, 29, 5, 1, 1, 1, 17, 5, 1, 37, 1, 13, 5, 41, 1, 1, 1, 5, 1, 1, 1, 1, 5, 17, 13, 53, 1, 5, 1, 1, 29, 1, 5, 61, 1, 1, 1, 65, 1, 1, 17, 1, 5, 1, 1, 73, 37, 5, 1, 1, 13, 1, 5, 1, 41, 1, 1, 85, 1, 29, 1

Offset: 1

N. J. A. Sloane, Dec 22 2009

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A170818, A170819, A097706, A083025, A170824, A170825.

a:= n-> mul (i, i=map (x-> x[1], select (x-> isprime (x[1]) and irem (x[1], 4)=1, ifactors(n)[2]))): seq (a(n), n=1..120);

Table[Times@@Select[Transpose[FactorInteger[n]][[1]],Mod[#,4]==1&], {n,90}] (* Harvey P. Dale, Dec 07 2012 *)

a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i,1] % 4 == 1, f[i,1], 1));} \\ Amiram Eldar, Jun 09 2025

Corrected and extended with Maple program by Alois P. Heinz, Dec 23 2009

cp's OEIS Frontend

A181860 a(n) = lcm(n^2, swinging_factorial(n)).

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A343431 Part of n composed of prime factors of the form 6k-1.

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A170817 a(n) = product of distinct primes of form 4k+1 that divide n.

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