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A305895 Filter sequence combining sum of proper divisors (A001065) and cototient (A051953) of n. 2
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, 20, 2, 21, 2, 22, 23, 24, 25, 26, 2, 27, 28, 29, 2, 30, 2, 31, 32, 33, 2, 34, 35, 36, 37, 38, 2, 39, 28, 40, 41, 42, 2, 43, 2, 44, 45, 46, 47, 48, 2, 49, 50, 51, 2, 52, 2, 53, 54, 55, 47, 56, 2, 57, 58, 59, 2, 60, 41, 61, 62, 63, 2, 64, 37, 65, 66, 67, 68, 69, 2, 70, 71, 72, 2, 73, 2, 74, 75 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Restricted growth sequence transform of ordered pair [A001065(n), A051953(n)].

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

FORMULA

a(1) = 1; for n > 1, a(n) = 1 + A295885(n).

PROG

(PARI)

up_to = 65537;

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; };

A001065(n) = (sigma(n)-n);

A051953(n) = (n-eulerphi(n));

Aux305895(n) = [A001065(n), A051953(n)];

v305895 = rgs_transform(vector(up_to, n, Aux305895(n)));

A305895(n) = v305895[n];

CROSSREFS

Cf. A001065, A051953, A295885, A305800.

Differs from A300249 for the first time at n=105, where a(105) = 75, while A300249(105) = 56.

Differs from A300235 for the first time at n=153, where a(153) = 110, while A300235(153) = 106.

Sequence in context: A319348 A300249 A300235 * A327931 A300833 A300243

Adjacent sequences:  A305892 A305893 A305894 * A305896 A305897 A305898

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 14 2018

STATUS

approved

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Last modified October 22 14:44 EDT 2019. Contains 328318 sequences. (Running on oeis4.)