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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A331738

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

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Last modified September 20 16:50 EDT 2021. Contains 347586 sequences. (Running on oeis4.)