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

1,4

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

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

Example

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.

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);

Prog

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

Crossrefs

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

Sequence in context: A329376 A336643 A334039 * A071974 A056622 A375568

Adjacent sequences: A076930 A076931 A076932 * A076934 A076935 A076936

Keyword

nonn

Author

Amarnath Murthy, Oct 18 2002

Extensions

More terms from Sascha Kurz, Jan 21 2003

Status

approved