A388276 Numbers k for which A053585(sigma(k)) is equal to A053585(k) and that satisfy also Euler's condition for odd perfect numbers (A228058).

117, 10309, 92781, 134749, 257725, 360937, 505141, 796797, 835029, 1148881, 1212741, 1247389, 2319525, 3248433, 3368725, 4546269, 4966677, 6602701, 6725201, 9023425, 9597529, 10339929, 10914669, 11226501, 12326221, 12628525, 16304629, 17685913, 19919925, 20875725, 24921493, 25774633, 28722025, 29235897, 29817121

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..200

Index entries for sequences where odd perfect numbers must occur, if they exist at all.

Prog

(PARI)
is_A228058(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));
is_A388275(k) = if(1==k, 1, my(f=factor(k), x=f[#f~, 1]^f[#f~, 2], s = sigma(f)); if(s%x, 0, my(f=factor(s), y=f[#f~, 1]^f[#f~, 2]); (x==y)));
is_A388276(k) = (is_A388275(k) && is_A228058(k));

Crossrefs

Intersection of A228058 and A388275.

Cf. A000203, A053585, A388274.

Cf. also A386428.

Sequence in context: A218416 A027511 A385161 * A203626 A220600 A194613

Adjacent sequences: A388273 A388274 A388275 * A388277 A388278 A388279

Keyword

nonn

Author

Antti Karttunen, Sep 20 2025

Status

approved