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

Author

Antti Karttunen, Aug 28 2025

Keywords

• nonn
• new

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)

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.

Programs

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));