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URL: https://oeis.org/A388997

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A388997
Numbers satisfying Euler's condition for odd perfect numbers, divided by their largest squarefree divisor: a(n) = A003557(A228058(n)).
2
3, 3, 3, 7, 3, 5, 3, 3, 27, 5, 3, 3, 11, 7, 3, 5, 3, 7, 13, 3, 3, 5, 3, 3, 5, 27, 3, 5, 3, 27, 3, 7, 17, 5, 3, 11, 3, 3, 3, 19, 7, 5, 7, 11, 3, 3, 3, 21, 5, 3, 27, 3, 5, 3, 5, 3, 7, 3, 23, 5, 3, 5, 3, 13, 15, 7, 27, 3, 3, 3, 27, 3, 5, 3, 11, 3, 7, 3, 243, 3, 5, 17, 3, 15, 3, 5, 3, 3, 3, 29, 27, 5, 7, 11, 5, 3, 3, 19
OFFSET
1,1
LINKS
FORMULA
a(n) = A003557(A228058(n)).
a(n) = A228058(n) / A389167(n).
PROG
(PARI)
up_to = 20000;
isA228058(n) = if(!(n%2)||(omega(n)<2), 0, my(f=factor(n), y=0); for(i=1, #f~, if(1==(f[i, 2]%4), if((1==y)||(1!=(f[i, 1]%4)), return(0), y=1), if(f[i, 2]%2, return(0)))); (y));
A228058list(up_to) = { my(v=vector(up_to), k=0, n=0); while(k<up_to, n++; if(isA228058(n), k++; v[k] = n)); (v); };
v228058 = A228058list(up_to);
A228058(n) = v228058[n];
A003557(n) = (n/factorback(factor(n)[, 1]));
CROSSREFS
Cf. also A389166.
Sequence in context: A214834 A291767 A135087 * A294505 A242016 A084038
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 29 2025
STATUS
approved