The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A281685 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A281685

Numbers k such that A001221(k) = A001221(A003415(k)).
(history; published version)

#12 by N. J. A. Sloane at Sun Apr 23 23:59:34 EDT 2017

STATUS

proposed

approved

#11 by G. C. Greubel at Sun Apr 23 21:11:32 EDT 2017

STATUS

editing

proposed

#10 by G. C. Greubel at Sun Apr 23 21:11:24 EDT 2017

MATHEMATICA

a[n_] := If[Abs@n < 2, 0, n Total[#2/#1 & @@@ FactorInteger[Abs@n]]];

Select[Range[100], PrimeNu[#] == PrimeNu[a[#]] &] (* G. C. Greubel, Apr 23 2017 *)

STATUS

approved

editing

#9 by Peter Luschny at Fri Jan 27 17:21:37 EST 2017

STATUS

reviewed

approved

#8 by Michel Marcus at Fri Jan 27 15:10:32 EST 2017

STATUS

proposed

reviewed

#7 by Colin Barker at Fri Jan 27 13:51:47 EST 2017

STATUS

editing

proposed

#6 by Colin Barker at Fri Jan 27 13:51:32 EST 2017

LINKS

Colin Barker, <a href="/A281685/b281685.txt">Table of n, a(n) for n = 1..1000</a>

STATUS

approved

editing

#5 by N. J. A. Sloane at Fri Jan 27 12:32:43 EST 2017

STATUS

proposed

approved

#4 by Colin Barker at Fri Jan 27 11:09:34 EST 2017

STATUS

editing

proposed

Discussion

Fri Jan 27

11:16

R. J. Cano: Interesting...

#3 by Colin Barker at Fri Jan 27 11:08:51 EST 2017

NAME

allocated for Colin BarkerNumbers k such that A001221(k) = A001221(A003415(k)).

DATA

4, 16, 18, 20, 21, 24, 26, 27, 33, 35, 38, 40, 44, 45, 48, 50, 51, 52, 56, 57, 62, 63, 65, 68, 69, 74, 75, 76, 77, 80, 85, 86, 91, 92, 93, 95, 96, 98, 99, 104, 106, 108, 111, 115, 117, 119, 122, 123, 126, 129, 133, 134, 135, 136, 141, 143, 144, 145, 146, 147

OFFSET

1,1

COMMENTS

Numbers k such that the number of distinct prime divisors of k is equal to the number of distinct prime divisors of the arithmetic derivative of k.

PROG

(PARI) arde(n) = sum(i=1, #f=factor(n)~, n/f[1, i]*f[2, i])

select(k->omega(k)==omega(arde(k)), vector(200, k, k+1))

CROSSREFS

Cf. A001221, A003415, A209870, A281686.

KEYWORD

allocated

nonn

AUTHOR

Colin Barker, Jan 27 2017

STATUS

approved

editing