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A061380
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Triangular numbers with product of digits also a triangular number.
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0
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0, 1, 3, 6, 10, 66, 105, 120, 153, 190, 210, 231, 300, 351, 406, 465, 630, 703, 741, 780, 820, 903, 990, 1035, 1081, 1326, 1540, 1770, 1830, 2016, 2080, 2556, 2701, 2850, 3003, 3081, 3160, 3240, 3403, 3570, 4005, 4095, 4560, 4950, 5050, 5460, 5671, 6105
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OFFSET
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1,3
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LINKS
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EXAMPLE
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153 is a triangular number and the product of digits 15 is also a triangular number.
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MAPLE
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q:= n-> (l-> issqr(1+8*mul(i, i=l)))(convert(n, base, 10)):
select(q, [seq(i*(i+1)/2, i=0..110)])[]; # Alois P. Heinz, Mar 17 2023
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PROG
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(Magma) [t: n in [0..110] | IsSquare(8*p+1) where p is &*Intseq(t) where t is (n*(n+1) div 2)]; // Bruno Berselli, Jun 30 2011
(PARI) isok(k) = ispolygonal(k, 3) && ispolygonal(vecprod(digits(k)), 3); \\ Michel Marcus, Mar 17 2023
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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