A374204 a(n) is the minimum value of A347381 that it obtains among divisors of n larger than 1. By convention a(1) = 0.

0, 0, 1, 0, 1, 0, 3, 0, 1, 0, 3, 0, 2, 0, 1, 0, 6, 0, 5, 0, 1, 0, 7, 0, 1, 0, 1, 0, 8, 0, 10, 0, 1, 0, 1, 0, 4, 0, 1, 0, 10, 0, 9, 0, 1, 0, 13, 0, 3, 0, 1, 0, 15, 0, 1, 0, 1, 0, 15, 0, 7, 0, 1, 0, 1, 0, 12, 0, 1, 0, 19, 0, 9, 0, 1, 0, 3, 0, 19, 0, 1, 0, 20, 0, 1, 0, 1, 0, 22, 0, 2, 0, 1, 0, 1, 0, 24, 0, 1, 0, 20

Offset: 1

Author

Antti Karttunen, Jul 07 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A347381, A374214.

Cf. also A374196.

Programs

PARI

A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A252463(n) = if(!(n%2),n/2,A064989(n));
A347381(n) = if(1==n,0, my(lista=List([]), i, k=n, stemvec, stemlen, sbr=sigma(n)); while(k>1, listput(lista,k); k = A252463(k)); stemvec = Vecrev(Vec(lista)); stemlen = #stemvec; while(1, if((i=vecsearch(stemvec,sbr))>0, return(stemlen-i)); sbr = A252463(sbr)));
A374204(n) = { my(m=-1,x); fordiv(n,d,if(d>1, x = A347381(d); if(m<0 || x
				

Formula

a(1) = 0, and for n > 1, a(n) = Min_{d|n, d>1} A347381(d).

For nonprime n, a(n) = min(A347381(n), A374214(n)).