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

Author

Antti Karttunen, Jun 14 2018

Keywords

• nonn

Comments

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

Links

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

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.

Programs

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];

Formula

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