perplexus.info :: Numbers : Introducing sphenic numbers

Introducing sphenic numbers (Posted on 2018-10-14)

A sphenic number S.N. is a product of three distinct prime numbers.

a. Clearly each S.N. has 8 divisors. Show that not only S.N.s claim this feature.
b. Find the smallest consecutive pair n,n+1 of sphenic numbers.
c. Same for the smallest triplet.
d. Prove that sphenic quadruplet n,n+1,n+2,n+3 is "mission impossible".

No Solution Yet Submitted by Ady TZIDON

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Parts a, d (spoiler)

| Comment 1 of 3

a) p^7 has 8 divisors if p is prime.

Also p*q^3, where p and q are prime

b) ?

c) ?

d) one of n, n+1, n+2, n+3 must be divisible by 4, and thus cannot be sphenic

Posted by Steve Herman on 2018-10-14 09:27:24

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