This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A274262 #13 Jan 05 2025 19:51:40 %S A274262 1,2,4,6,8,12,12,18,20,24,20,44,24,36,48,54,32,76,36,88,72,60,44,156, %T A274262 72,72,100,132,56,208,60,162,120,96,144,316,72,108,144,312,80,312,84, %U A274262 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 %N A274262 Number of positive integers possessing exactly n Fibonacci representations (A000121). %H A274262 Zai-Qiao Bai and Steven R. Finch, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/54-4/BaiFinch09122016.pdf">Fibonacci and Lucas Representations</a>, Fibonacci Quart. 54 (2016), no. 4, 319-326. %F A274262 Let p, q, r be distinct primes and k be a positive integer. %F A274262 If n = p^k then a(n) = 2*(p-1)*(2*p-1)^(k-1). %F A274262 If n = p*q then a(n) = 6*(p-1)*(q-1). %F A274262 If n = p^2*q then a(n) = 2*(p-1)*(8*p-5)*(q-1). %F A274262 If n = p^3*q then a(n) = 2*(p-1)*(2*p-1)*(10*p-7)*(q-1). %F A274262 If n = p^4*q then a(n) = 6*(p-1)*(2*p-1)^2*(4*p-3)*(q-1). %F A274262 If n = p^2*q^2 then a(n) = 2*(p-1)*(q-1)*(26*p*q-18*p-18*q+13). %F A274262 If n = p*q*r then a(n) = 26*(p-1)*(q-1)*(r-1). %e A274262 Let phi denote the Euler totient. %e A274262 The integer p^2*q has 8 multiplicative compositions: %e A274262 (p^2*q), p^2*q, q*p^2, p*(p*q), (p*q)*p, q*p*p, p*q*p, p*p*q %e A274262 from which %e A274262 a(p^2*q) = 2*(3*phi(p^2)*phi(q) + 5*phi(p)^2*phi(q)) %e A274262 follows immediately. %Y A274262 Cf. A000121, A067595. %K A274262 nonn %O A274262 1,2 %A A274262 _Steven Finch_, Jun 16 2016