cp's OEIS Frontend

A244397 Consider a number n with m decimal digits, m>1. The sequence lists the numbers n such that the prefix of length m-1 and the suffix of length m-1 have both the same distinct prime divisors.

%I A244397 #20 Nov 10 2024 02:22:28
%S A244397 22,24,28,33,39,42,44,48,55,66,77,82,84,88,93,99,111,124,164,222,248,
%T A244397 333,444,526,548,555,666,724,777,842,888,999,1111,1248,1664,2162,2222,
%U A244397 2500,2855,3200,3333,3600,3748,4324,4444,4864,5042,5128,5555,5768,5882
%N A244397 Consider a number n with m decimal digits, m>1. The sequence lists the numbers n such that the prefix of length m-1 and the suffix of length m-1 have both the same distinct prime divisors.
%C A244397 Let x(0)x(1)...x(q-1)x(q) denote the decimal expansion of a number n. The sequence lists the numbers n such that the prefix p = x(0)x(1)...x(q-1) and the suffix x(1)...x(q-1)x(q) have the same prime distinct divisors.
%e A244397 3748 is in the sequence because 374 and 748 have the same prime divisors: {2,11,17}.
%p A244397 with(numtheory):
%p A244397 for n from 10 to 10000 do:
%p A244397       x:=convert(n, base, 10):n1:=nops(x):
%p A244397       s1 := n mod 10^ilog10(n):
%p A244397       s2:=(n-irem(n,10))/10:
%p A244397       x1:=factorset(s1):x2:=factorset(s2):
%p A244397       if x1 = x2 and x1 <>{}
%p A244397         then
%p A244397         printf(`%d, `, n):
%p A244397         else
%p A244397       fi:
%p A244397 od:
%Y A244397 Cf. A244394.
%K A244397 nonn,base
%O A244397 1,1
%A A244397 _Michel Lagneau_, Jun 27 2014