A327964 a(1) = 1, and for n > 1, a(n) = A276085(A327963(n)).

1, 0, 0, 4, 0, 6, 0, 8, 3, 30, 0, 12, 0, 4, 15, 16, 0, 32, 0, 20, 7, 2310, 0, 24, 7, 8, 27, 28, 0, 6469693230, 0, 32, 31, 510510, 35, 36, 0, 32, 39, 40, 0, 7420738134810, 0, 44, 2312, 12, 0, 48, 31, 10, 51, 52, 0, 54, 55, 56, 211, 6469693230, 0, 60, 0, 212, 30032, 64, 5, 1922760350154212639070, 0, 68, 2311, 32589158477190044730, 0, 72, 0, 2312, 216, 76, 5

Offset: 1

Author

Antti Karttunen, Oct 07 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..2048

Crossrefs

Cf. A002110, A003415, A129251, A276085, A276086, A327963, A328113.

Cf. A327929 (a subsequence of fixed points).

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A129251(n) = { my(f = factor(n)); sum(k=1, #f~, (f[k, 2]>=f[k, 1])); };
A276086(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };
A327963(n) = if(1==n,0,my(u=A003415(n)); if(!A129251(u),u,A276086(n)));
A002110(n) = prod(i=1,n,prime(i));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
A327964(n) = if(1==n,n,A276085(A327963(n)));

Formula

a(1) = 1, and for n > 1, a(n) = A276085(A327963(n)).

a(p) = 0 for all primes p.

a(A327929(n)) = A327929(n) for all n. [But note that there are also other fixed points.]