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.
The top left 15x6 corner of the array: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 2, 4, 4, 8, 6, 8, 8, 16, 10, 12, 12, 16, 14, 16, 16 3, 6, 5, 12, 7, 10, 9, 24, 11, 18, 13, 20, 15, 18, 17 4, 8, 5, 16, 9, 10, 9, 32, 17, 14, 13, 20, 17, 22, 17 5, 10, 6, 20, 8, 12, 11, 40, 12, 20, 14, 24, 21, 18, 19 6, 12, 6, 24, 10, 14, 10, 48, 18, 16, 19, 28, 16, 20, 18
A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ This function from M. F. Hasler A007947(n) = factorback(factorint(n)[, 1]); \\ Andrew Lelechenko, May 09 2014 A065642(n) = { my(r=A007947(n)); if(1==n,n,n = n+r; while(A007947(n) <> r, n = n+r); n); }; A285321bi(row,col) = if(1==row,A019565(col),A065642(A285321bi(row-1,col))); A002260(n)= { n-binomial((sqrtint(8*n)+1)\2, 2); }; \\ M. F. Hasler, Mar 10 2014 A004736(n)= { 1 + binomial(1 + floor(1/2 + sqrt(2*n)), 2) - n; }; A285321(n) = A285321bi(A002260(n), A004736(n)); A048675(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; \\ Michel Marcus, Oct 10 2016 A285325(n) = A048675(A285321(n)); for(n=1, 120, write("b285325.txt", n, " ", A285325(n)));
(define (A285325 n) (A285325bi (A002260 n) (A004736 n))) (define (A285325bi row col) (A048675 (A285321bi row col)))
A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ This function from M. F. Hasler A007947(n) = factorback(factorint(n)[, 1]); \\ From Andrew Lelechenko, May 09 2014 A065642(n) = { my(r=A007947(n)); if(1==n,n,n = n+r; while(A007947(n) <> r, n = n+r); n); }; A285323(n) = A065642(A065642(A019565(n))) / A019565(n);
from operator import mul from sympy import prime, primefactors from functools import reduce def a019565(n): return reduce(mul, (prime(i+1) for i, v in enumerate(bin(n)[:1:-1]) if v == '1')) if n > 0 else 1 # This function from Chai Wah Wu def a007947(n): return 1 if n<2 else reduce(mul, primefactors(n)) def a065642(n): if n==1: return 1 r=a007947(n) n += r while a007947(n)!=r: n+=r return n def a(n): return a065642(a065642(a019565(n)))//a019565(n) print([a(n) for n in range(101)]) # Indranil Ghosh, Apr 20 2017
(define (A285323 n) (/ (A065642 (A065642 (A019565 n))) (A019565 n))) (define (A285323 n) (cond ((zero? n) 1) ((or (= 1 (A000120 n)) (> (A000040 (+ 1 (A285099 n))) (A000290 (A000040 (+ 1 (A007814 n)))))) (A000290 (A000040 (+ 1 (A007814 n))))) (else (A000040 (+ 1 (A285099 n))))))
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