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A228363
Sorted entries of the multiplication table a*b, with a>1, b>1.
2
4, 6, 6, 8, 8, 9, 10, 10, 12, 12, 12, 12, 14, 14, 15, 15, 16, 16, 16, 18, 18, 18, 18, 20, 20, 20, 20, 21, 21, 22, 22, 24, 24, 24, 24, 24, 24, 25, 26, 26, 27, 27, 28, 28, 28, 28, 30, 30, 30, 30, 30, 30, 32, 32, 32, 32, 33, 33, 34, 34, 35, 35, 36, 36, 36, 36, 36, 36, 36, 38, 38, 39, 39, 40, 40, 40, 40
OFFSET
1,1
COMMENTS
Consists of the composite numbers (A002808), with the composite nonsquares (A089229) occurring more than once, i.e., the n-th composite appears A144925(n) times.
A complement of the primes (A000040).
PROG
(PARI) L=listcreate(); for(k=2, 250, for(l=2, 250, listput(L, k*l))); v=vecsort(Vec(L)); for(n=1, 100, print1(v[n], ", "))
(Python)
from math import isqrt
from sympy import composite
from oeis_sequences.OEISsequences import bisection, bsearch
def A228363(n):
if n == 1: return 4
def g(x): return x-((m:=composite(x))<<1)+1-(s:=isqrt(m))**2+(sum(m//k for k in range(1, s+1))<<1)
def f(x): return n+bsearch(g, x)
return composite(bisection(f, n+1, n+1)-n+1) # Chai Wah Wu, Mar 01 2026
CROSSREFS
Cf. A061017 (sorted entries of standard multiplication table)
Sequence in context: A070259 A111653 A372786 * A383618 A334289 A173395
KEYWORD
nonn
AUTHOR
Ralf Stephan, Aug 21 2013
STATUS
approved