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A307812
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Triangular numbers t(n) with a zeroless decimal representation such that (product of decimal digits of t(n)) / n is an integer.
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1
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1, 6, 15, 465, 666, 23436, 93528, 198765, 664128, 1493856, 1786995, 2767128, 2953665, 18292176, 23891328, 44655975, 169878528, 787667895, 859984128, 1934948736, 3333238776, 97844944896, 237295393965, 292957233975, 379244291328, 175847359339575, 12999674534178816
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OFFSET
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1,2
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COMMENTS
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Are all terms of the sequence bigger than 1 divisible by 3? I conjecture that 1 and 15 are the only terms for which (product of decimal digits of t(n)) = n.
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LINKS
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EXAMPLE
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For n = 30, t(30) = 465, product of decimal digits of t(30) = 4*6*5 = 120, product of decimal digits of t(n) / n = 120 / 30 = 4 so t(30) = 465 is in the sequence.
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MATHEMATICA
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idx = Select[Range[100000], Product[j, {j, IntegerDigits[#*(# + 1)/2]}] != 0 && Divisible[Product[j, {j, IntegerDigits[#*(# + 1)/2]}], #] &]; idx*(idx + 1)/2 (* Vaclav Kotesovec, Apr 30 2019 *)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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