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 A198255 Number of ways to write n as the sum of two coprime squarefree semiprimes. 1
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 1, 0, 1, 0, 2, 0, 5, 0, 0, 0, 1, 0, 3, 1, 2, 0, 3, 0, 4, 1, 0, 1, 3, 0, 5, 0, 2, 0, 4, 0, 1, 2, 2, 0, 3, 0, 4, 2, 2, 1, 3, 0, 6, 1, 2, 0, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,41 COMMENTS This sequence is term by term less than or equal to A197629. The first odd term where the inequality is strict is the 97th term. The first even term that is strictly less than A197629 is the 248th term. There are interesting bands in the scatterplot of this sequence. - Antti Karttunen, Sep 23 2018 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 EXAMPLE Same as A197629 until a(97) since 97=(2)(3)(7)+(5)(11) and thus the value of the 97th term of A197629 is one greater. The 248th term of A197629 is the first even term which is one greater since 248=(3)(5)(7)+(11)(13). From Antti Karttunen, Sep 23 2018: (Start) For n = 97 there are following six solutions: 97 = 6+91 = 10+87 = 15+82 = 35+62 = 39+58 = 46+51, thus a(97) = 6. For n = 248 there are following seven solutions: 248 = 33+215 = 35+213 = 39+209 = 65+183 = 87+161 = 115+133 = 119+129, thus a(248) = 7. (End) PROG (MATLAB) function [asubn] = sps(n) % Returns the number of coprime, squarefree, semiprime, partitions a+b of n. r = 0; % r is the number of sps's of n k=6; while k < n/2, if gcd(k, n-k)==1 if length(factor(k)) == 2 if length(factor(n-k)) == 2 if prod(diff(factor(k)))*prod(diff(factor(n-k))) > 0 r = r + 1; end end end end k = k + 1; end asubn = r; end (PARI) A198255(n) = sum(k=4, (n-1)\2, gcd(k, n-k)==1&&(2==bigomega(k))&&(2==bigomega(n-k))&&issquarefree(k)&&issquarefree(n-k)); \\ Antti Karttunen, Sep 23 2018, after Charles R Greathouse IV's program for A197629 CROSSREFS Cf. A197629. Sequence in context: A318982 A069851 A197629 * A290542 A359300 A029834 Adjacent sequences: A198252 A198253 A198254 * A198256 A198257 A198258 KEYWORD nonn,look AUTHOR Jason Holland, Oct 22 2011 STATUS approved

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Last modified September 9 16:40 EDT 2024. Contains 375765 sequences. (Running on oeis4.)