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A325809 Let k = A228058(n). a(n) is the number of ways to partition the divisors of k into complementary subsets x and y so that the (k-Sum(x)) and (k-Sum(y)) are coprime. 3
8, 12, 8, 16, 8, 15, 16, 8, 113, 16, 8, 15, 16, 7, 14, 8, 8, 13, 16, 15, 8, 15, 14, 8, 15, 254, 8, 16, 8, 128, 16, 16, 16, 15, 8, 15, 16, 15, 8, 16, 13, 15, 7, 13, 16, 8, 16, 43008, 8, 8, 126, 8, 15, 15, 15, 8, 16, 8, 14, 8, 15, 16, 8, 16, 60672, 15, 256, 13, 16, 7, 103, 16, 16, 8, 16, 16, 16, 8, 2015, 16, 8, 15, 16, 39093, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The smallest value known so far occurs as a(449) = 6. A228058(449) = 23837 = 11^2 * 197.
LINKS
FORMULA
a(n) = A325807(A228058(n)).
PROG
(PARI)
up_to = 25000;
isA228058(n) = if(!(n%2)||(omega(n)<2), 0, my(f=factor(n), y=0); for(i=1, #f~, if(1==(f[i, 2]%4), if((1==y)||(1!=(f[i, 1]%4)), return(0), y=1), if(f[i, 2]%2, return(0)))); (y));
A228058list(up_to) = { my(v=vector(up_to), k=0, n=0); while(k<up_to, n++; if(isA228058(n), k++; v[k] = n)); (v); };
v228058 = A228058list(up_to);
A228058(n) = v228058[n];
A325807(n) = { my(divs=divisors(n), s=sigma(n), r); sum(b=0, (2^(-1+length(divs)))-1, r=sumbybits(divs, 2*b); (1==gcd(n-(s-r), n-r))); };
sumbybits(v, b) = { my(s=0, i=1); while(b>0, s += (b%2)*v[i]; i++; b >>= 1); (s); };
CROSSREFS
Sequence in context: A160862 A152077 A215696 * A173461 A335160 A295782
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 25 2019
STATUS
approved

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Last modified April 14 07:58 EDT 2024. Contains 371655 sequences. (Running on oeis4.)