A389200 a(n) = A351568(A228058(n)), where A351568(x) is the sum of divisors of the largest unitary divisor of x that is a square, and A228058 gives the numbers satisfying Euler's condition for odd perfect numbers.

13, 13, 13, 57, 13, 31, 13, 13, 121, 31, 13, 13, 133, 57, 13, 31, 13, 57, 183, 13, 13, 31, 13, 13, 31, 121, 13, 31, 13, 121, 13, 57, 307, 31, 13, 133, 13, 13, 13, 381, 57, 31, 57, 133, 13, 13, 13, 741, 31, 13, 121, 13, 31, 13, 31, 13, 57, 13, 553, 31, 13, 31, 13, 183, 403, 57, 121, 13, 13, 13, 121, 13, 31, 13, 133

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to sigma(n).

Formula

a(n) = A000203(A389160(n)) = A351568(A228058(n)).

a(n) = A389203(n) / A389201(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];
A350388(n) = { my(m=1, f=factor(n)); for(k=1, #f~, if(0==(f[k, 2]%2), m *= (f[k, 1]^f[k, 2]))); (m); };
A351568(n) = sigma(A350388(n));
A389200(n) = A351568(A228058(n));

Crossrefs

Cf. A000203, A228058, A351568, A389160, A389201, A389203.

Contains only terms of A065768\{1}.

Sequence in context: A290686 A291569 A290854 * A254928 A294657 A201773

Adjacent sequences: A389197 A389198 A389199 * A389201 A389202 A389203

Keyword

nonn

Author

Antti Karttunen, Sep 28 2025

Status

approved