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 A326377 #10 Jul 06 2019 02:20:51 %S A326377 1,2,3,4,11,12,29,8,81,1100,59,48,101,195478444,40425,16,157,648,229, %T A326377 440000,64240097649,1445390468875226977004,313,192,214358881, %U A326377 44574662297516497591170630280506162081362246142404,19683,9921285858330292941824,421,72765000,547,32 %N A326377 For any number n > 0, let f(n) be the polynomial of a single indeterminate x where the coefficient of x^e is the prime(1+e)-adic valuation of n (where prime(k) denotes the k-th prime); f establishes a bijection between the positive numbers and the polynomials of a single indeterminate x with nonnegative integer coefficients; let g be the inverse of f; a(n) = g(f(n) o f(n)) (where o denotes function composition). %C A326377 This sequence is the main diagonal of A326376. %F A326377 a(n) = A326376(n, n). %F A326377 a(2^k) = 2^k for any k >= 0. %F A326377 a(3^k) = A060722(k) for any k >= 0. %F A326377 a(prime(k)) = A243896(k) for any k >= 1 (where prime(k) denotes the k-th prime number). %e A326377 The first terms, alongside the corresponding polynomials, are: %e A326377 n a(n) f(n) f(n) o f(n) %e A326377 -- ---- ----- ----------- %e A326377 1 1 0 0 %e A326377 2 2 1 1 %e A326377 3 3 x x %e A326377 4 4 2 2 %e A326377 5 11 x^2 x^4 %e A326377 6 12 x+1 x+2 %e A326377 7 29 x^3 x^9 %e A326377 8 8 3 3 %e A326377 9 81 2*x 4*x %e A326377 10 1100 x^2+1 x^4+2*x^2+2 %e A326377 11 59 x^4 x^16 %e A326377 12 48 x+2 x+4 %o A326377 (PARI) g(p) = my (c=Vecrev(Vec(p))); prod (i=1, #c, if (c[i], prime(i)^c[i], 1)) %o A326377 f(n, v='x) = my (f=factor(n)); sum (i=1, #f~, f[i, 2] * v^(primepi(f[i, 1]) - 1)) %o A326377 a(n) = g(f(n, f(n))) %Y A326377 Cf. A060722, A243896, A326376. %K A326377 nonn %O A326377 1,2 %A A326377 _Rémy Sigrist_, Jul 02 2019