A325376 Terms k of A228058 such that gcd(k - A048250(k), A162296(k) - k) = A162296(k) - k.

153, 477, 801, 1773, 2097, 2421, 3725, 4041, 4689, 4753, 5013, 5337, 6309, 6957, 7281, 7929, 8577, 8725, 9549, 9873, 11225, 11493, 13437, 14357, 14409, 14733, 15381, 17001, 17973, 18621, 19269, 19917, 21213, 21537, 23481, 24777, 25101, 25749, 26073, 26225, 26721, 27369, 28989, 29161, 29313, 29961, 31225, 32229, 32553, 33849

Offset: 1

Author

Antti Karttunen, Apr 22 2019

Keywords

• nonn

Comments

Also, terms of this sequence are A228058(k) for all such k that A325375(k) = A325320(k).

In range 1 .. 2^27 there are no such terms k of A228058 that gcd(k-A048250(k), A162296(k)-k) = k - A048250(k).

If any odd perfect number exists, then it must occur in this sequence, but should also satisfy the other condition given above.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12532
• Index entries for sequences where any odd perfect numbers must occur

Crossrefs

Cf. A048250, A162296, A228058, A325313, A325314, A325320, A325375, A325822.

Programs

PARI

A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
A162296(n) = sumdiv(n, d, d*(1-issquarefree(d)));
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));
k=0; n=0; while(k<100,n++; if(isA228058(n) && (gcd(n-A048250(n),A162296(n)-n) == A162296(n)-n),k++; print1(n,", ")));