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A255346
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Numbers n such that n and n+1 both have at least two distinct prime factors.
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17
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14, 20, 21, 33, 34, 35, 38, 39, 44, 45, 50, 51, 54, 55, 56, 57, 62, 65, 68, 69, 74, 75, 76, 77, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 98, 99, 104, 105, 110, 111, 114, 115, 116, 117, 118, 119, 122, 123, 129, 132, 133, 134, 135, 140, 141, 142, 143, 144, 145, 146, 147, 152, 153, 154
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OFFSET
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1,1
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COMMENTS
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These numbers provide solutions to the problem of finding (x,y) such that x(x+1) | y(y+1) but none of x or x+1 divides any of y or y+1. Namely, these solutions are given for (x,y) being members of the sequence such that x(x+1) divides y(y+1), the smallest of which are (14,20), (14,35), (20,35), ... but, e.g., (14,69) is excluded since 14 | 70.
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LINKS
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PROG
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(PARI) for(n=2, 199, omega(n)>=2||(n++&&next); omega(n-1)>=2&&print1((n-1)", "))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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