A305895 Filter sequence combining sum of proper divisors (A001065) and cototient (A051953) of n.

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

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: A300235 A373379 A351260 * A327931 A369050 A300833

Adjacent sequences: A305892 A305893 A305894 * A305896 A305897 A305898

Keyword

nonn

Author

Antti Karttunen, Jun 14 2018

Status

approved