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

1,1

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.

Links

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

Example

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.

Mathematica

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

Crossrefs

A000005, A033950, A081381, A235524

Sequence in context: A031632 A097767 A031520 * A249227 A130181 A158325

Adjacent sequences: A235522 A235523 A235524 * A235526 A235527 A235528

Keyword

nonn

Author

Walter Roscello, Jan 11 2014

Status

approved