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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.)