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Search: a176556 -id:a176556
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Replace n with concatenation of its divisors.
+10
58
1, 12, 13, 124, 15, 1236, 17, 1248, 139, 12510, 111, 1234612, 113, 12714, 13515, 124816, 117, 1236918, 119, 12451020, 13721, 121122, 123, 1234681224, 1525, 121326, 13927, 12471428, 129, 12356101530, 131, 12481632, 131133, 121734, 15735, 123469121836, 137
OFFSET
1,2
COMMENTS
a(n) is the union of A176555(n) for n >= 1 and A176556(n) for n >= 2. See A176553 (numbers m such that concatenations of divisors of m are noncomposites) and A176554 (numbers m such that concatenations of divisors of m are nonprimes). [Jaroslav Krizek, Apr 21 2010]
a(n) is the concatenation of n-th row of the triangle in A027750.
LINKS
FORMULA
A134681(n) = A055642(a(n)). - Reinhard Zumkeller, Nov 06 2007
MATHEMATICA
a[n_] := ToExpression[ StringJoin[ ToString /@ Divisors[n] ] ]; Table[ a[n], {n, 1, 34}] (* Jean-François Alcover, Dec 01 2011 *)
FromDigits[Flatten[IntegerDigits/@Divisors[#]]]&/@Range[40] (* Harvey P. Dale, Nov 09 2012 *)
PROG
(Haskell)
a037278 = read . concatMap show . a027750_row :: Integer -> Integer
-- Reinhard Zumkeller, Jul 13 2013, May 01 2012, Aug 07 2011
(PARI) a(n) = my(s=""); fordiv(n, d, s = concat(s, Str(d))); eval(s); \\ Michel Marcus, Jun 01 2019 and Sep 22 2022
(Magma) k:=1; sol:=[];
for u in [1..34] do D:=Divisors(u); conc:=D[1];
for u1 in [2..#D] do a:=#Intseq(conc); a1:=#Intseq(D[u1]); conc:=10^a1*conc+D[u1]; end for;
sol[u]:=conc; k:=k+1;
end for;
sol; // Marius A. Burtea, Jun 01 2019
(MATLAB) m=1;
for u=1:34 div=divisors(u); conc=str2num(strrep(num2str(div), ' ', ''));
sol(m)=conc; m=m+1;
end
sol % Marius A. Burtea, Jun 01 2019
(Python)
from sympy import divisors
def a(n): return int("".join(str(d) for d in divisors(n)))
print([a(n) for n in range(1, 35)]) # Michael S. Branicky, Dec 31 2020
CROSSREFS
KEYWORD
nonn,easy,base,nice,changed
EXTENSIONS
More terms from Erich Friedman
STATUS
approved
Numbers n such that concatenations of divisors of n are nonprime.
+10
5
1, 2, 4, 5, 6, 8, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 80, 81
OFFSET
1,2
COMMENTS
See A037278(n) = concatenation of divisors of n. See A176556 for corresponding values of concatenations. Complement of A176553(n) for n >= 2.
LINKS
EXAMPLE
a(6) = 8: divisors of 8 are 1,2,4,8 and their concatenation 1248 is nonprime.
MATHEMATICA
Select[Range[100], !PrimeQ[FromDigits[Flatten[IntegerDigits/@ Divisors[ #]]]]&] (* Harvey P. Dale, Jul 09 2021 *)
KEYWORD
nonn,base
AUTHOR
Jaroslav Krizek, Apr 20 2010
EXTENSIONS
Edited and extended by Charles R Greathouse IV, Apr 30 2010
STATUS
approved

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