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A076412 Number of n's in A076411. 2
1, 3, 4, 1, 7, 9, 2, 5, 4, 13, 15, 17, 19, 21, 4, 3, 16, 25, 27, 20, 9, 18, 13, 33, 35, 19, 18, 39, 41, 43, 28, 17, 47, 49, 51, 53, 55, 57, 59, 61, 39, 24, 65, 67, 69, 71, 35, 38, 75, 77, 79, 81, 47, 36, 85, 87, 89, 23, 68, 71, 10, 12, 95, 97, 99, 101, 103, 40, 65, 107, 109, 100 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Equals {1} union A053289. - Tom Verhoeff, Jan 06 2008

Further comments from Tom Verhoeff, Jan 06 2008: (Start)

In general, for any nonnegative increasing sequence A (offset 1), i.e., with 0 <= A(i) < A(i+1), define

F = 'first differences of A' (offset 1), i.e., F(n) = A(n+1) - A(n)

L = 'number of A(i) less than n' (offset 1)

M = 'number of values at most n in L' (offset 0; auxiiliary sequence)

N = 'number of n's in L' (offset 0). Then M = A, i.e. M(k) = A(k+1), N = [ A(1) ] union F.

Proof: Observe that L is nonnegative and ascending: 0 <= L(i) <= L(i+1).

M(0) = N(0) = number of 0's in L = number of i >= 0 such that no A(j) < i = min A = A(1)

For k > 0, M(k) = number of values at most k in L = A(k+1)

N(k) = number of k's in L = number i >= 0 such that exactly k A(j) < i = M(k) - M(k-1) = A(k+1) - A(k) = F(k). QED (End)

First difference of perfect powers: A001597 prepended by 1. - Robert G. Wilson v, May 21 2009

Question: Does every number appear at least once? See the comment in A053289. - Robert G. Wilson v, May 21 2009

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 0..10488

EXAMPLE

a(9)=13 because 9 appears 13 times in A076411.

MATHEMATICA

t = Join[{0, 1}, Select[ Range@ 3600, GCD @@ Last /@ FactorInteger@# > 1 &]]; Rest@t - Most@t (* Robert G. Wilson v, May 21 2009 *)

CROSSREFS

Cf. A001597, A076411.

Cf. A053289.

Sequence in context: A262216 A076446 A053289 * A053707 A075052 A111516

Adjacent sequences:  A076409 A076410 A076411 * A076413 A076414 A076415

KEYWORD

nonn

AUTHOR

Zak Seidov, Oct 09 2002

EXTENSIONS

a(19)-a(71) from Robert G. Wilson v, May 21 2009

STATUS

approved

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Last modified May 26 16:50 EDT 2020. Contains 334627 sequences. (Running on oeis4.)