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 A076446 Differences of consecutive powerful numbers (definition 1). 4
 3, 4, 1, 7, 9, 2, 5, 4, 13, 15, 8, 9, 19, 8, 13, 4, 3, 16, 25, 27, 4, 16, 9, 18, 13, 32, 1, 35, 19, 18, 31, 8, 32, 9, 43, 16, 12, 17, 47, 49, 23, 27, 1, 53, 55, 16, 41, 23, 36, 61, 7, 4, 28, 24, 65, 36, 27, 4, 69, 71, 27, 8, 21, 17, 3, 72, 77, 47, 32, 81, 47, 36, 36, 49, 87, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The term 1 appears infinitely often. Erdos conjectured that two consecutive 1's do not occur. (see Guy). REFERENCES R. K. Guy, Unsolved Problems in Number Theory, B16 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Powerful numbers FORMULA A001694[n+1]-A001694[n] EXAMPLE The first two powerful numbers are 1 and 4, there difference is 3, so a(1)=3. MATHEMATICA Differences[Join[{1}, Select[Range[2000], Min[FactorInteger[#][[All, 2]]]>1&]]] (* Harvey P. Dale, Aug 27 2017 *) PROG (Haskell) a076446 n = a076446_list !! (n-1) a076446_list = zipWith (-) (tail a001694_list) a001694_list -- Reinhard Zumkeller, Nov 30 2012 CROSSREFS Cf. A001694, A076444. Sequence in context: A202500 A016607 A262216 * A053289 A076412 A053707 Adjacent sequences:  A076443 A076444 A076445 * A076447 A076448 A076449 KEYWORD nonn AUTHOR Jud McCranie, Oct 15 2002 STATUS approved

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Last modified January 26 14:08 EST 2020. Contains 331280 sequences. (Running on oeis4.)