A235525 Numbers which have identical primes in n and d(n) but are not refactorable.

486, 768, 8748, 303750, 354294, 393216, 480000, 506250, 984150, 1179648, 1228800, 1417176, 3906250, 5467500, 6635520, 9841500, 18750000, 24504606, 25312500, 35156250, 47829690, 57177414, 57395628, 83886080, 90354432, 123018750, 153600000, 154140672, 156243654, 201326592, 210937500, 221433750, 245760000, 258280326, 382637520, 460800000, 492075000, 600000000

Offset: 1

Author

Walter Roscello, Jan 11 2014

Keywords

• nonn

Comments

Numbers in A081381 that are not in A033950.

Although the set of primes in d(n) and n are identical, there is at least one prime occurring with a higher power in d(n) than in n.

Examples

			486 = 2^1 * 3^5 therefore d(486) = 2 * 6 = 2^2 * 3^1
768 = 2^8 * 3^1 therefore d(768) = 9 * 2 = 2^1 * 3^2
Each has the same set of primes in n and d(n) but has too many of one of the primes in d(n) to be refactorable.
		

Links

• Walter Roscello and Giovanni Resta, Table of n, a(n) for n = 1..100 (first 50 terms from Walter Roscello)

Crossrefs

A000005, A033950, A081381, A235524

Programs

Mathematica

Select[Range[10^6], Mod[#, t = DivisorSigma[0, #]] > 0 && First /@ FactorInteger[#] == First /@ FactorInteger[t] &] (* Giovanni Resta, Jan 11 2014 *)