A387166 Numbers k for which gcd(k, A003961(k)) = gcd(sigma(k), A003961(k)) > 1, and that satisfy Euler's condition for odd perfect numbers (A228058).

14157, 33525, 101025, 118825, 129605, 281025, 300713, 301725, 335405, 348525, 358925, 438525, 573525, 618525, 686025, 688205, 696725, 742577, 776025, 838125, 909225, 911025, 978525, 1046025, 1079225, 1099805, 1226025, 1293525, 1316025, 1322893, 1428889, 1451025, 1529045, 1563525, 1698525, 1721025, 1788525, 1991025, 2036025

Offset

1,1

Links

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

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
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));
isA349176(n) = if(!(n%2), 0, my(u=A003961(n), t=gcd(u, n)); (t>1)&&(gcd(u, sigma(n))==t));
isA387166(n) = (isA228058(n) && isA349176(n));

Crossrefs

Intersection of A228058 and A349176.

Intersection of A387164 and A104210, or equally, intersection of A387164 and A349166.

Setwise difference A387164 \ A387167.

Cf. A000203, A003961.

Sequence in context: A207289 A249192 A204282 * A134610 A104825 A184574

Adjacent sequences: A387163 A387164 A387165 * A387167 A387168 A387169

Keyword

nonn

Author

Antti Karttunen, Aug 28 2025

Status

approved