A346088 -id:A346088 - cp's OEIS frontend

A346089 a(n) = n divided by the smallest divisor d of n for which A002034(d) = A002034(n), where A002034(n) is the smallest positive integer k such that k! is a multiple of n.

1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 3, 1, 1, 2, 1, 4, 3, 2, 1, 6, 1, 2, 1, 4, 1, 6, 1, 1, 3, 2, 5, 4, 1, 2, 3, 8, 1, 6, 1, 4, 5, 2, 1, 3, 1, 2, 3, 4, 1, 2, 5, 8, 3, 2, 1, 12, 1, 2, 9, 2, 5, 6, 1, 4, 3, 10, 1, 8, 1, 2, 3, 4, 7, 6, 1, 5, 3, 2, 1, 12, 5, 2, 3, 8, 1, 10, 7, 4, 3, 2, 5, 3, 1, 2, 9, 4, 1, 6, 1, 8, 15

Offset: 1

Antti Karttunen, Jul 05 2021

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Cf. A002034, A345935, A345936, A345944 (positions of 1's), A346088.
Cf. also A344759.
Differs from A302776 for the first time at n=27, where a(27) = 1, while A302776(27) = 3.

A002034(n) = if(1==n,n,my(s=factor(n)[, 1], k=s[#s], f=Mod(k!, n)); while(f, f*=k++); (k)); \\ After code in A002034.
A346089(n) = { my(x=A002034(n)); fordiv(n,d,if(A002034(d)==x, return(n/d))); };

a(n) = n / A346088(n).

A354998 Smallest divisor d of n for which A344005(d) = A344005(n), where A344005(n) is the smallest positive integer m such that n divides m*(m+1).

Original entry on oeis.org

1, 1, 3, 4, 5, 3, 7, 8, 9, 5, 11, 4, 13, 7, 15, 16, 17, 9, 19, 5, 7, 11, 23, 24, 25, 13, 27, 28, 29, 15, 31, 32, 33, 17, 35, 9, 37, 19, 13, 40, 41, 7, 43, 44, 45, 23, 47, 16, 49, 25, 51, 13, 53, 27, 11, 8, 19, 29, 59, 60, 61, 31, 63, 64, 65, 33, 67, 17, 69, 35, 71, 9, 73, 37, 25, 76, 77, 13, 79, 16, 81, 41, 83, 84

Offset: 1

Antti Karttunen, Jun 17 2022

nonn

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A344005, A354991, A354992, A354999.

Cf. also A344758, A346088.

s[n_] := Module[{m = 1}, While[! Divisible[m*(m + 1), n], m++]; m]; a[n_] := Module[{sn = s[n], ds = Divisors[n]}, Do[If[s[d] == sn, Return[d]], {d, ds}]]; Array[a, 100] (* Amiram Eldar, Jun 17 2022 *)

A344005(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m))); \\ From A344005
A354998(n) = { my(x=A344005(n)); fordiv(n, d, if(A344005(d)==x, return(d))); };

a(n) = n / A354999(n).

cp's OEIS Frontend

A346089 a(n) = n divided by the smallest divisor d of n for which A002034(d) = A002034(n), where A002034(n) is the smallest positive integer k such that k! is a multiple of n.

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