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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. 2
 1, 4, 9, 1521, 3600, 7396, 8100, 103041, 120409, 160801, 11471769, 11655396, 12802084, 15210000, 22724289, 36000000, 42889401, 42928704, 45481536, 45968400, 46009089, 54567769, 61811044, 62236321, 70006689, 73925604, 73960000, 76965529, 79174404, 81000000, 85008400, 97693456, 97713225, 100000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..3730 FORMULA a(n) = A153745(n)^2. PROG (Python) from sympy import divisors from gmpy2 import is_prime, isqrt, isqrt_rem, is_square A258660_list = [] for l in range(1, 17): ....if not is_prime(l): ........fs = divisors(l) ........a, b = isqrt_rem(10**(l-1)) ........if b > 0: ............a += 1 ........for n in range(a, isqrt(10**l-1)+1): ............n2 = n**2 ............ns = str(n2) ............for g in fs: ................y = 0 ................for h in range(0, l, g): ....................y += int(ns[h:h+g]) ................if not is_square(y): ....................break ............else: ................A258660_list.append(n2) # Chai Wah Wu, Jun 08 2015 CROSSREFS Cf. A153745. Sequence in context: A179935 A073172 A168139 * A260305 A229338 A111443 Adjacent sequences:  A258657 A258658 A258659 * A258661 A258662 A258663 KEYWORD base,nonn AUTHOR Doug Bell, Jun 06 2015 EXTENSIONS Corrected a(13)-a(14) by Chai Wah Wu, Jun 08 2015 STATUS approved

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Last modified March 18 16:00 EDT 2019. Contains 321292 sequences. (Running on oeis4.)