A387167 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).

117, 153, 333, 369, 425, 477, 549, 637, 657, 845, 873, 909, 925, 1017, 1053, 1233, 1325, 1377, 1413, 1421, 1445, 1525, 1557, 1629, 1737, 1773, 1805, 1813, 1825, 2009, 2097, 2169, 2225, 2313, 2493, 2525, 2529, 2597, 2637, 2725, 2817, 2825, 2853, 2989, 2997, 3033, 3177, 3321, 3357, 3425, 3509, 3573, 3577, 3609, 3725

Offset: 1

Author

Antti Karttunen, Aug 28 2025

Keywords

• nonn
• new

Comments

Terms k of A228058 for which k and A003961(k) are relatively prime, and also sigma(k) and A003961(k) are coprime.

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 A349177.

Intersection of A387164 and A319630, or equally, intersection of A387164 and A349165.

Setwise difference A387164 \ A387166.

Cf. A000203, A003961.

Subsequence of A387164 from which this differs for the first time at n=201, where a(201) = 14225, while A387164(201) = 14157.

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));
isA349177(n) = if(!(n%2),0,my(u=A003961(n),t=gcd(u,n)); (1==t)&&(gcd(u,sigma(n))==t));
isA387167(n) = (isA228058(n) && isA349177(n));