A334542 - OEIS

A334542

Numbers m such that m^2 = p^2 + k^2, with p > 0, where p = A007954(m) = the product of digits of m.

%I #23 Jul 17 2021 03:47:13

%S 1,2,3,4,5,6,7,8,9,58,85,375,666,1968,1998,3578,3665,3891,4658,4995,

%T 6675,7735,18434,27475,28784,46692,56763,58896,59577,59949,76965,

%U 186633,186673,795848,949968,965667,1339575,1587616,1929798,2765388,2989584,3674195,4763568,5762784,36741656,58988961,134369685,188959392

%N Numbers m such that m^2 = p^2 + k^2, with p > 0, where p = A007954(m) = the product of digits of m.

%H Giovanni Resta, <a href="/A334542/b334542.txt">Table of n, a(n) for n = 1..140</a> (terms < 2*10^13)

%e 58 is a term as p = 5*8 = 40 and 58^2 = 3364 = 40^2 + 42^2.

%e 3891 is a term as p = 3*8*9*1 = 216 and 3891^2 = 15139881 = 216^2 + 3885^2.

%o (PARI) isok(m) = my(p=vecprod(digits(m))); p && issquare(m^2 - p^2); \\ _Michel Marcus_, May 06 2020

%Y Cf. A007954, A000404, A078134, A334557, A334558.

%Y Subsequence of A052382 (zeroless numbers).

%K nonn,base

%O 1,2

%A _Scott R. Shannon_, May 05 2020