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
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Oct 18 2002
EXTENSIONS
More terms from Sascha Kurz, Jan 21 2003
STATUS
approved