A324544 a(n) = A009194(A250246(n)) = gcd(A250246(n), A324545(n)).

1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 4, 1, 2, 3, 1, 1, 3, 1, 2, 1, 2, 1, 12, 1, 2, 1, 28, 1, 6, 1, 1, 3, 2, 1, 1, 1, 2, 3, 10, 1, 6, 1, 4, 1, 2, 1, 4, 1, 1, 1, 2, 1, 6, 1, 8, 1, 2, 1, 12, 1, 2, 1, 1, 1, 18, 1, 2, 15, 2, 1, 3, 1, 2, 3, 4, 1, 6, 1, 2, 3, 2, 1, 4, 1, 2, 3, 4, 1, 3, 1, 4, 1, 2, 1, 12, 1, 1, 1, 1, 1, 6, 1, 2, 1

Offset: 1

Author

Antti Karttunen, Mar 06 2019

Keywords

• nonn

Comments

Fixed points are: 1, 6, 28, 120, 496, 8128, etc,

Positions where a(n) == A250246(n) are: 1, 6, 28, 120, 496, 864, 8128, 11424, 15240, ..., which is sequence A250245(A007691(n)) sorted into ascending order.

Links

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

Crossrefs

Cf. A007691, A009194, A250246, A252754, A324394, A324545, A324546.

Differs from A009194 for the first time at n=39. Here a(39) = 3.

Programs

PARI

up_to = 65537;
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
A020639(n) = if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1); \\ From A020639
A055396(n) = if(1==n,0,primepi(A020639(n)));
v078898 = ordinal_transform(vector(up_to,n,A020639(n)));
A078898(n) = v078898[n];
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A250246(n) = if(1==n,n,my(k = 2*A250246(A078898(n)), r = A055396(n)); if(1==r, k, while(r>1, k = A003961(k); r--); (k)));
A009194(n) = gcd(n, sigma(n));
A324544(n) = A009194(A250246(n));

Formula

a(n) = A009194(A250246(n)) = gcd(A250246(n), A324545(n)).

a(n) = A324394(A252754(n)).