

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
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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 !! (n1)
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



