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A258660 Numbers n such that the number of digits d in n is not prime and for each factor f of d the sum of the d/f digit groupings of size f is a square.

%I A258660 #14 May 22 2025 10:21:43
%S A258660 1,4,9,1521,3600,7396,8100,103041,120409,160801,11471769,11655396,
%T A258660 12802084,15210000,22724289,36000000,42889401,42928704,45481536,
%U A258660 45968400,46009089,54567769,61811044,62236321,70006689,73925604,73960000,76965529,79174404,81000000,85008400,97693456,97713225,100000000
%N A258660 Numbers n such that the number of digits d in n is not prime and for each factor f of d the sum of the d/f digit groupings of size f is a square.
%C A258660 If a(n) has m = p^k digits, then a(n)*10^((p-1)*m) is also a member of the sequence.  For instance, 1521*10^(2^k-4) is in the sequence for all integers k >=2. # _Chai Wah Wu_, Jun 08 2015
%H A258660 Chai Wah Wu, <a href="/A258660/b258660.txt">Table of n, a(n) for n = 1..3730</a>
%F A258660 a(n) = A153745(n)^2.
%o A258660 (Python)
%o A258660 from sympy import divisors
%o A258660 from gmpy2 import is_prime, isqrt, isqrt_rem, is_square
%o A258660 A258660_list = []
%o A258660 for l in range(1,17):
%o A258660     if not is_prime(l):
%o A258660         fs = divisors(l)
%o A258660         a, b = isqrt_rem(10**(l-1))
%o A258660         if b > 0:
%o A258660             a += 1
%o A258660         for n in range(a,isqrt(10**l-1)+1):
%o A258660             n2 = n**2
%o A258660             ns = str(n2)
%o A258660             for g in fs:
%o A258660                 y = 0
%o A258660                 for h in range(0,l,g):
%o A258660                     y += int(ns[h:h+g])
%o A258660                 if not is_square(y):
%o A258660                     break
%o A258660             else:
%o A258660                 A258660_list.append(n2) # _Chai Wah Wu_, Jun 08 2015
%Y A258660 Cf. A153745.
%K A258660 base,nonn
%O A258660 1,2
%A A258660 _Doug Bell_, Jun 06 2015
%E A258660 Corrected a(13)-a(14) by _Chai Wah Wu_, Jun 08 2015