A076933 Final number obtained when n is divided by its divisors starting from the smallest one in increasing order until one no longer gets an integer.

1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 10, 1, 1, 1, 1, 5, 1, 1, 14, 1, 1, 1, 4, 1, 1, 1, 6, 1, 1, 1, 1, 1, 7, 1, 22, 3, 1, 1, 2, 7, 5, 1, 26, 1, 9, 1, 1, 1, 1, 1, 10, 1, 1, 3, 1, 1, 11, 1, 34, 1, 1, 1, 3, 1, 1, 5, 38, 1, 13, 1, 2, 3, 1, 1, 14, 1, 1, 1, 11, 1, 3, 1, 46, 1, 1, 1, 4, 1, 7, 33

Offset: 1

Author

Amarnath Murthy, Oct 18 2002

Keywords

• nonn

Comments

a(n) = 1 if n = p, n = p^3, n = p*q or n = k! for some k, or n = p*q*r where the product of two primes is more than the third, where p q and r are primes. Question: What is the longest string of ones in this sequence? Subsidiary sequence: Index of the start of the first occurrence of a string of n ones.

Concerning this question, see also A329549. Furthermore as a(8k+4) > 1 such a string can have at most length 7. - David A. Corneth, Nov 16 2019

Examples

			a(12) = 2: the divisors of 12 in increasing order are 1,2,3,4,6,12. and 12/1 = 12, 12/2 = 6, 6/3 = 2 that is the final integer, as the next divisor 4 > 2.
		

Links

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

Crossrefs

Cf. A240694 (partial products of divisors of n), A329377 (number of iterations needed to reach the final number), A329549.

Programs

Maple

for i from 1 to 200 do d := sort(convert(divisors(i),list)):j := 1:g := i: while((g mod d[j])=0) do g := g/d[j]:j := j+1: if(j>nops(d)) then break:fi: od:a[i] := g:od:seq(a[k],k=1..200);

PARI

A076933(n) = { my(k=n); fordiv(k,d,if(n%d,return(n),n /= d)); (n); }; \\ Antti Karttunen, Nov 16 2019

Extensions

More terms from Sascha Kurz, Jan 21 2003