A336552 -id:A336552 - cp's OEIS frontend

A336550 Numbers k such that A007947(k) divides sigma(k) and A003557(k)-1 either divides A326143(k) [= A001065(k) - A007947(k)], or both are zero.

6, 24, 28, 96, 120, 234, 384, 496, 936, 1536, 1638, 6144, 8128, 24576, 42588, 98304, 393216, 1089270, 1572864, 6291456, 25165824, 33550336, 100663296, 115048440, 402653184, 1185125760, 1610612736

Offset: 1

Antti Karttunen, Jul 28 2020

Numbers k such that gcd(sigma(k)-A007947(k), A007947(k)) == A007947(k) are those in A175200. These are equal to k such that gcd(A326143(k), A007947(k)) = gcd(sigma(k)-A007947(k)-k, A007947(k)) are equal to A007947(k).
Sequence is infinite because all numbers of the form 6*4^n (A002023) are present.
Question: Are there any odd terms?

Index entries for sequences where odd perfect numbers must occur, if they exist at all

Intersection of A175200 and A336552.
Cf. A007947, A326143, A336551.
Cf. A000396, A002023, A326145 (subsequences).
Cf. also A336641 for a similar construction.

A007947(n) = factorback(factorint(n)[, 1]);
isA336550(n) = { my(r=A007947(n), s=sigma(n), u=((n/r)-1)); (!(s%r) && (gcd(u,(s-r-n))==u)); };

A336553 Odd numbers k such that gcd(A336551(k), A326143(k)) is equal to A336551(k).

Original entry on oeis.org

45, 63, 99, 117, 147, 153, 171, 207, 261, 279, 315, 325, 333, 369, 387, 423, 425, 477, 495, 531, 549, 585, 603, 639, 657, 693, 711, 725, 735, 747, 765, 801, 819, 847, 855, 873, 909, 925, 927, 963, 981, 1017, 1025, 1035, 1071, 1125, 1143, 1179, 1197, 1233, 1251, 1287, 1305, 1325, 1341, 1359, 1395, 1413, 1449, 1467, 1503

Offset: 1

Antti Karttunen, Jul 28 2020

nonn

Is the intersection with A336554 empty?

Odd terms in A336552.

Cf. A336554.

A007947(n) = factorback(factorint(n)[, 1]);
A326143(n) = (sigma(n)-A007947(n)-n);
A336551(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 2] = f[i, 2]-1); (factorback(f)-1); };
isA336553(n) = if(!(n%2),0, my(u=A336551(n)); (u==gcd(u,A326143(n))));

cp's OEIS Frontend

A336550 Numbers k such that A007947(k) divides sigma(k) and A003557(k)-1 either divides A326143(k) [= A001065(k) - A007947(k)], or both are zero.

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