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A327963
If A327928(n) > 0, a(n) = A276086(n), otherwise a(n) = A003415(n).
9
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
1,4
COMMENTS
After zero, sequence contains only terms of A048103.
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)).
PROG
(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)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 07 2019
STATUS
approved