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 A274262 Number of positive integers possessing exactly n Fibonacci representations (A000121). 1
 1, 2, 4, 6, 8, 12, 12, 18, 20, 24, 20, 44, 24, 36, 48, 54, 32, 76, 36, 88, 72, 60, 44, 156, 72, 72, 100, 132, 56, 208, 60, 162, 120, 96, 144, 316, 72, 108, 144, 312, 80, 312, 84, 220, 304, 132, 92, 540, 156, 280, 192, 264, 104, 460, 240, 468, 216, 168, 116, 116, 120, 180, 456, 486, 288, 520, 132, 352, 264, 624, 140 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Zai-Qiao Bai and Steven R. Finch, Fibonacci and Lucas Representations, Fibonacci Quart. 54 (2016), no. 4, 319-326. FORMULA Let p, q, r be distinct primes and k be a positive integer. If n = p^k then a(n) = 2*(p-1)*(2*p-1)^(k-1). If n = p*q then a(n) = 6*(p-1)*(q-1). If n = p^2*q then a(n) = 2*(p-1)*(8*p-5)*(q-1). If n = p^3*q then a(n) = 2*(p-1)*(2*p-1)*(10*p-7)*(q-1). If n = p^4*q then a(n) = 6*(p-1)*(2*p-1)^2*(4*p-3)*(q-1). If n = p^2*q^2 then a(n) = 2*(p-1)*(q-1)*(26*p*q-18*p-18*q+13). If n = p*q*r then a(n) = 26*(p-1)*(q-1)*(r-1). EXAMPLE Let phi denote the Euler totient. The integer p^2*q has 8 multiplicative compositions: (p^2*q), p^2*q, q*p^2, p*(p*q), (p*q)*p, q*p*p, p*q*p, p*p*q from which a(p^2*q) = 2*(3*phi(p^2)*phi(q) + 5*phi(p)^2*phi(q)) follows immediately. CROSSREFS Cf. A000121, A067595. Sequence in context: A068065 A278228 A028328 * A092990 A323505 A350355 Adjacent sequences: A274259 A274260 A274261 * A274263 A274264 A274265 KEYWORD nonn AUTHOR Steven Finch, Jun 16 2016 STATUS approved

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Last modified February 5 03:48 EST 2023. Contains 360082 sequences. (Running on oeis4.)