cp's OEIS Frontend

A062892 Number of squares that can be obtained by permuting the digits of n.

%I A062892 #26 Oct 19 2021 23:51:16
%S A062892 1,1,0,0,1,0,0,0,0,1,1,0,0,0,0,0,1,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
%T A062892 0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,0,1,1,0,0,0,
%U A062892 0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,2,0,0,0,0
%N A062892 Number of squares that can be obtained by permuting the digits of n.
%C A062892 The original definition was ambiguous (it did not specify how repeated digits or leading zeros are to be handled). Here is a precise version (based on the Mathematica code):
%C A062892 Suppose the decimal expansion of n has d digits. Apply all d! permutations, discard duplicates, but keep any with leading zeros; now ignore leading zeros; a(n) is the number of squares on the resulting list. For example, if n = 100 we end up with 100, 010, 001, and both 100 and 1 are squares, so a(100)=2. If n=108 we get 6 numbers but only (0)81 is a square, so a(108)=1. - _N. J. A. Sloane_, Jan 16 2014
%H A062892 David A. Corneth, <a href="/A062892/b062892.txt">Table of n, a(n) for n = 0..9999</a>
%F A062892 a(A096600(n))=0; a(A007937(n))>0; a(A096599(n))=1; a(A096598(n))>1. - _Reinhard Zumkeller_, Jun 29 2004
%e A062892 a(169) = 3; the squares obtained by permuting the digits are 169, 196, 961.
%t A062892 Table[t1=Table[FromDigits[k],{k,Permutations[IntegerDigits[n]]}]; p=Length[Select[t1,IntegerQ[Sqrt[#]]&]], {n,0,104}] (* _Jayanta Basu_, May 17 2013 *)
%o A062892 (PARI) a(n) = {my(d = vecsort(digits(n)), res = 0); forperm(d, p, res += issquare(fromdigits(Vec(p)))); res } \\ _David A. Corneth_, Oct 18 2021
%o A062892 (Python)
%o A062892 from math import isqrt
%o A062892 from sympy.utilities.iterables import multiset_permutations as mp
%o A062892 def sqr(n): return isqrt(n)**2 == n
%o A062892 def a(n):
%o A062892     s = str(n)
%o A062892     perms = (int("".join(p)) for p in mp(s, len(s)))
%o A062892     return len(set(p for p in perms if sqr(p)))
%o A062892 print([a(n) for n in range(105)] ) # _Michael S. Branicky_, Oct 18 2021
%Y A062892 A096599 gives the squares k^2 such that a(k^2) = 1.
%K A062892 base,nonn,easy
%O A062892 0,101
%A A062892 _Amarnath Murthy_, Jun 29 2001
%E A062892 Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jul 02 2001