A069149 -id:A069149 - cp's OEIS frontend

A069150 Integers of the form k*k!/A062758(k) in the order they appear in A069149, where A062758(k) is the product of squares of divisors of k.

1, 1, 2, 24, 720, 4480, 3628800, 1925, 479001600, 387459072, 20922789888000, 6402373705728000, 5516784599040000, 1124000727777607680000, 135277939046250, 24817936069329577574400, 553211880832106496000000

Offset: 1

Benoit Cloitre, Apr 08 2002

Cf. A062758, A069149.

Rest[Select[Table[k! k/(Times@@Divisors[k])^2,{k,30}],IntegerQ]] (* Harvey P. Dale, Oct 17 2020 *)
Select[(# * #! / #^DivisorSigma[0, #]) & /@ Range[1, 30], IntegerQ] (* Amiram Eldar, Jul 16 2022 *)

for(n=1,30,if((n*(n!))%(n^numdiv(n))==0,print1((n*(n!))/(n^numdiv(n)),",")))

Name clarified by Amiram Eldar, Jul 16 2022

Missing a(1)=1 inserted by Sean A. Irvine, Apr 06 2024

A069148 Numbers k such that k*k!/A062758(k) is not an integer where A062758(k) is the product of squares of divisors of k.

Original entry on oeis.org

4, 6, 8, 10, 14, 16, 18, 20, 22, 26, 28, 34, 38, 42, 44, 46, 52, 58, 62, 66, 68, 74, 76, 78, 82, 86, 92, 94, 102, 106, 114, 116, 118, 122, 124, 134, 138, 142, 146, 148, 158, 164, 166, 172, 174, 178, 186, 188, 194, 202, 206, 212, 214, 218, 222, 226, 236, 244, 246

Offset: 1

Benoit Cloitre, Apr 08 2002

Amiram Eldar, Table of n, a(n) for n = 1..10000

Complement of A069149.

Cf. A001563 (n*n!), A062758.

Rest[Position[Table[(n*n!)/(Times@@Divisors[n])^2,{n,250}],?(!IntegerQ[ #]&)]//Flatten] (* _Harvey P. Dale, Apr 24 2019 *)
Select[Range[250], !Divisible[#!, #^(DivisorSigma[0, #] - 1)] &] (* Amiram Eldar, Jul 07 2022 *)

for(n=1,320,if((n*(n!))%(n^numdiv(n))>0,print1(n,",")))

cp's OEIS Frontend

A069150 Integers of the form k*k!/A062758(k) in the order they appear in A069149, where A062758(k) is the product of squares of divisors of k.

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