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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.)