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A235525
Numbers which have identical primes in n and d(n) but are not refactorable.
2
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
KEYWORD
nonn
AUTHOR
Walter Roscello, Jan 11 2014
STATUS
approved