The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A300245

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A300245

Filter sequence combining arithmetic derivative (A003415) with its Möbius transform (A300251).
(history; published version)

#11 by OEIS Server at Sat Mar 24 18:53:41 EDT 2018

LINKS

Antti Karttunen, <a href="/A300245/b300245_1.txt">Table of n, a(n) for n = 1..65537</a>

#10 by N. J. A. Sloane at Sat Mar 24 18:53:41 EDT 2018

STATUS

proposed

approved

Discussion

Sat Mar 24

18:53

OEIS Server: Installed new b-file as b300245.txt.  Old b-file is now b300245_1.txt.

#9 by Antti Karttunen at Fri Mar 16 14:35:50 EDT 2018

STATUS

editing

proposed

#8 by Antti Karttunen at Fri Mar 16 14:11:15 EDT 2018

COMMENTS

Restricted growth sequence transform of P(A003415(n), A300251(n)), where P(a,b) is a two-argument form of A000027 used as a Cantor pairing function N x N -> N.

Restricted growth sequence transform of ordered pair [A003415(n), A300251(n)].

LINKS

Antti Karttunen, <a href="/A300245/b300245_1.txt">Table of n, a(n) for n = 1..65537</a>

PROG

Aux300245(n) = if(1==n, 0, (1/2)*(2 + ((A003415(n)+A300251(n))^2) - A003415(n) - 3*A300251(n)));

Aux300245(n) = [A003415(n), A300251(n)];

STATUS

proposed

editing

#7 by Jon E. Schoenfield at Tue Mar 13 23:04:30 EDT 2018

STATUS

editing

proposed

#6 by Jon E. Schoenfield at Tue Mar 13 23:04:26 EDT 2018

NAME

Filter sequence combining arithmetic derivative (A003415) with its Möbius- transform (A300251).

STATUS

proposed

editing

#5 by Antti Karttunen at Thu Mar 08 11:50:45 EST 2018

STATUS

editing

proposed

#4 by Antti Karttunen at Thu Mar 08 11:47:35 EST 2018

EXAMPLE

a(16) = a(28) (= 11) because both A003415(16) = A003415(28) = 32 and A300251(16) = A300251(28) = 20.

#3 by Antti Karttunen at Thu Mar 08 11:44:00 EST 2018

COMMENTS

Restricted growth sequence transform of P(A003415(n), A300251(n)), where P(a,b) is a two-argument form of A000027 used as a Cantor pairing function N x N -> N.

LINKS

Antti Karttunen, <a href="/A300245/b300245.txt">Table of n, a(n) for n = 1..65537</a>

CROSSREFS

Cf. A003415, A300249, A300251, A300252, A300253.

Discussion

Thu Mar 08

11:45

Antti Karttunen: Please do not shorten the data-section (the duplicated 36 is important).

#2 by Antti Karttunen at Thu Mar 08 11:19:57 EST 2018

NAME

allocated for Antti KarttunenFilter sequence combining arithmetic derivative (A003415) with its Möbius-transform (A300251).

DATA

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 17, 18, 19, 11, 2, 20, 2, 21, 22, 23, 24, 25, 2, 26, 27, 28, 2, 29, 2, 30, 31, 32, 2, 33, 34, 35, 36, 37, 2, 38, 27, 39, 40, 41, 2, 42, 2, 43, 44, 45, 46, 47, 2, 48, 49, 50, 2, 51, 2, 52, 53, 54, 46, 55, 2, 56, 57, 58, 2, 59, 40, 60, 61, 62, 2, 63, 36, 64, 65, 66

OFFSET

1,2

PROG

(PARI)

rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };

write_to_bfile(start_offset, vec, bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }

A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415

A300251(n) = sumdiv(n, d, moebius(n/d)*A003415(d));

Aux300245(n) = if(1==n, 0, (1/2)*(2 + ((A003415(n)+A300251(n))^2) - A003415(n) - 3*A300251(n)));

write_to_bfile(1, rgs_transform(vector(65537, n, Aux300245(n))), "b300245.txt");

CROSSREFS

Cf. A003415, A300251, A300252, A300253.

KEYWORD

allocated

nonn

AUTHOR

Antti Karttunen, Mar 08 2018

STATUS

approved

editing