A327963 If A327928(n) > 0, a(n) = A276086(n), otherwise a(n) = A003415(n).

0, 1, 1, 9, 1, 5, 1, 15, 6, 7, 1, 25, 1, 9, 150, 225, 1, 21, 1, 375, 10, 13, 1, 625, 10, 15, 3750, 5625, 1, 31, 1, 21, 14, 19, 126, 35, 1, 21, 210, 315, 1, 41, 1, 525, 39, 25, 1, 875, 14, 45, 5250, 7875, 1, 4375, 8750, 13125, 22, 31, 1, 49, 1, 33, 51, 441, 18, 61, 1, 735, 26, 59, 1, 1225, 1, 39, 55, 11025, 18, 71, 1, 18375, 36750, 43, 1, 30625, 22, 45

Offset: 1

Author

Antti Karttunen, Oct 07 2019

Keywords

• nonn

Comments

After zero, sequence contains only terms of A048103.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..2310
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A003415, A048103, A129251, A276085, A276086, A327859, A327928, A327929, A327964, A327965, A328097, A328098, A328099, A328113 (rgs-transform).

Cf. also A285330.

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)));

Formula

If A327928(n) > 0 [when n is one of the terms in A327929], then a(n) = A276086(n), otherwise a(n) = A003415(n).

For n > 1, a(n) = A276086(A327964(n)).