

A366066


a(n) is the largest positive integer k such that n can be expressed as the sum of k distinct positive integers that are coprime to each other.


1



0, 1, 1, 2, 2, 2, 3, 2, 3, 3, 3, 4, 3, 4, 3, 4, 4, 4, 5, 4, 5, 4, 5, 4, 5, 5, 5, 5, 5, 6, 5, 6, 5, 6, 5, 6, 6, 6, 6, 6, 6, 6, 7, 6, 7, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 9, 9, 9, 9, 9, 9, 9
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OFFSET

0,4


COMMENTS

The indices at which k first appears, for k >= 0: 1, 3, 6, 11, 18, 29, 42, 59, 78 (A014284). Such n's are expressed as the sum of 1 and the first primes.
Runs with length >= 2 start at numbers k^2  1 (k >= 2).
If there are terms between runs of k and k+1, these two numbers occur alternately. Suppose that m is such a term that is b(m) terms after the first occurrence of k+1; if b(m) is odd, there are at least two even numbers in the expression of n as the sum of k+1 integers, which are not coprime to each other, so a(m) = k.


LINKS



FORMULA

a(n) = A083375(n)  1 if and only if n = 7, 12, 14, 19, 21, 23, 30, 32, 34, 43, 45, 47, 60, 62, 79; otherwise, a(n) = A083375(n).


EXAMPLE

For n = 11, 1+2+3+5=11; so a(11) = 4.
For n = 12, 1+4+7=12; so a(12) = 3.


PROG

(PARI) lista(nn) = v=[0]; f=[7, 12, 14, 19, 21, 23, 30, 32, 34, 43, 45, 47, 60, 62, 79]; for(n=1, nn, for(i=1, prime(n), v=concat(v, n))); for(n=1, 15, v[f[n]+1]=v[f[n]+1]1); v;


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



