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 A304096 Number of Lucas numbers larger than 3 (4, 7, 11, 18, ...) that divide n. 6
 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 2, 1, 0, 0, 1, 1, 0, 1, 2, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 2, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 2, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,28 COMMENTS a(n) is the number of the divisors d of n that are of the form d = A000045(k-1) + A000045(k+1), for k >= 3. LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 FORMULA a(n) = Sum_{d|n, d>3} A102460(d). a(n) = A304094(n) - A079978(n) - 1. a(n) = A304092(n) - A059841(n) - A079978(n) - 1. a(n) = A007949(A304104(n)). EXAMPLE The divisors of 4 are 1, 2 and 4. Of these only 4 is a Lucas number larger than 3, thus a(4) = 1. The divisors of 28 are 1, 2, 4, 7, 14 and 28. Of these 4 and 7 are Lucas numbers (A000032) larger than 3, thus a(28) = 2. PROG (PARI) A102460(n) = { my(u1=1, u2=3, old_u1); if(n<=2, sign(n), while(n>u2, old_u1=u1; u1=u2; u2=old_u1+u2); (u2==n)); }; A304096(n) = sumdiv(n, d, (d>3)*A102460(d)); CROSSREFS Cf. A000032, A000045, A000204, A102460, A304092, A304094, A304095, A304104. Cf. also A005086, A300837. Sequence in context: A321888 A321750 A056929 * A151692 A280829 A303942 Adjacent sequences:  A304093 A304094 A304095 * A304097 A304098 A304099 KEYWORD nonn AUTHOR Antti Karttunen, May 13 2018 STATUS approved

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Last modified August 22 00:43 EDT 2019. Contains 326169 sequences. (Running on oeis4.)