A325979 Odd numbers k for which gcd(A325977(k), A325978(k)) is equal to abs(A325978(k)).

1, 3465, 72981, 78651, 80937, 152703, 199341, 201771, 241605, 253287, 492507, 631881, 880821, 933147, 985473, 1063755, 1209285, 1244133, 1292445, 1313235, 1327095, 1347885, 1360881, 1451835, 1521135, 1597365, 1620375, 1814373, 2015475, 2664585, 6058233, 6676371, 8186751, 11119761, 17496243, 18379935, 28695627

Offset: 1

Author

Antti Karttunen, Jun 02 2019

Keywords

• nonn

Comments

Provided that A325977(k) and A325978(k) are never zero for the same k, these are odd numbers k such that A325978(k) is not zero and divides A325977(k).

Of the first 281 terms, only a(5) = 80937, a(51) = 86086881, a(175) = 43024468437, and a(262) = 564858541521 are in A228058. - Updated Jul 20 2025

Links

• Giovanni Resta, Table of n, a(n) for n = 1..281 (terms < 10^12; first 65 terms from Antti Karttunen)
• Index entries for sequences where any odd perfect numbers must occur.

Crossrefs

Cf. A228058, A325975, A325977, A325978, A325981.

Programs

PARI

A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
A034460(n) = (A034448(n) - n);
A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
A325313(n) = (A048250(n) - n);
A325977(n) = ((A034460(n)+A325313(n))/2);
A162296(n) = sumdiv(n, d, d*(1-issquarefree(d)));
A325314(n) = (n - A162296(n));
A048146(n) = (sigma(n)-A034448(n));
A325814(n) = (n-A048146(n));
A325978(n) = ((A325314(n)+A325814(n))/2);
A325975(n) = gcd(A325977(n), A325978(n));
isA325979(n) = ((n%2)&&(A325975(n)==abs(A325978(n))));
\\ Or alternatively as:
isA325979(n) = if(!(n%2),0,my(x = A325977(n), y = A325978(n)); (!x&&!y)||(y&&!(x%y)));