A328112 a(1) = 0, for primes p, a(p) = 1, and for any other number n, a(n) = max(A003415(n), A276086(n)).

0, 1, 1, 9, 1, 5, 1, 15, 30, 45, 1, 25, 1, 75, 150, 225, 1, 125, 1, 375, 750, 1125, 1, 625, 1250, 1875, 3750, 5625, 1, 31, 1, 80, 42, 63, 126, 60, 1, 105, 210, 315, 1, 175, 1, 525, 1050, 1575, 1, 875, 1750, 2625, 5250, 7875, 1, 4375, 8750, 13125, 26250, 39375, 1, 92, 1, 147, 294, 441, 882, 245, 1, 735, 1470, 2205, 1, 1225, 1, 3675, 7350, 11025, 22050

Offset: 1

Author

Antti Karttunen, Oct 07 2019

Keywords

• nonn

Comments

Apart from primes p, for which a(p) = 1, the only duplicated values among the first 65537 terms are a(30040) = a(32344) = 51108 and a(30150) = a(60278) = 47685.

Examples

			As 30150 is not a prime, a(30150) = max(A003415(30150), A276086(30150)) = max(47685, 40817) = 47685.
As 60278 is not a prime, a(60278) = max(A003415(60278), A276086(60278)) = max(30141, 47685) = 47685.
		

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, A327858, A327859, A327928, A327929, A327963, A327965, A328097, A328098, A328099.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 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; };
A328112(n) = if(1==n,0,if(isprime(n),1,max(A003415(n),A276086(n))));