# Conjecture about the set of Sphenic numbers

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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Question 2: Instead of $\sum S_1$ you can write $$\sum_{k \in S_1} k.$$