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Sum of a set of sphenic numbers can't be equal to the sum of any other set of sphenic numbers.

By that I meant, Say S is the set of sphenic numbers. Let S$_1$ $\subset$ S. Then there is no such S$_2$ $\subset$ S so that,

S$_1$ $\neq$ S$_2$ AND $\sum S_1$ $=$ $\sum S_2$

Question 1 : Is this statement correct?

Question 2 : Is this formulation mathematically right? I mean even if the statement is wrong, is the way that I expressed it conveys mathematical notations/rules etc. Or, how a mathematician would write it if s/he intended to convey the same message?

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1) The statement is not correct. 230+1310=231+1309. Sphenic numbers gives the first sequential pair (and implies there are more) and the first run of three.

2) I'm not a mathematician, but the formulation seems fine to me. You might define Sphenic numbers so people don't have to look it up

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    @Ross: Yes, that is how I generated the example: using twin primes :-)2010-10-14
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Question 2: Instead of $\sum S_1$ you can write $\sum_{k \in S_1} k.$

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    I see. Thank you very much.2010-10-14