A389167 Largest squarefree number dividing the numbers satisfying Euler's condition for odd perfect numbers: a(n) = A007947(A228058(n)).

15, 39, 51, 35, 87, 65, 111, 123, 15, 85, 159, 183, 55, 91, 219, 145, 267, 119, 65, 291, 303, 185, 327, 339, 205, 39, 411, 265, 447, 51, 471, 203, 85, 305, 519, 143, 543, 579, 591, 95, 259, 365, 287, 187, 687, 699, 723, 105, 445, 771, 87, 807, 485, 831, 505, 843, 371, 879, 115, 545, 939, 565, 951, 221, 195, 427, 111

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..20410

Formula

a(n) = A228058(n) / A388997(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];
A007947(n) = factorback(factorint(n)[, 1]);
A389167(n) = A007947(A228058(n));

Crossrefs

Cf. A007947, A228058, A388997, A389164 [= sigma(a(n))].

Cf. also A389165.

Sequence in context: A320721 A086096 A272189 * A336560 A176257 A055131

Adjacent sequences: A389164 A389165 A389166 * A389168 A389169 A389170

Keyword

nonn

Author

Antti Karttunen, Sep 29 2025

Status

approved