A336553 -id:A336553 - cp's OEIS frontend

A336552 Numbers k such that A003557(k)-1 either divides A326143(k) [= A001065(k) - A007947(k)], or both are zero. Numbers k such that gcd(A336551(k), A326143(k)) is equal to A336551(k).

4, 6, 12, 20, 24, 28, 44, 45, 48, 52, 60, 63, 68, 76, 84, 90, 92, 96, 99, 116, 117, 120, 124, 126, 132, 140, 144, 147, 148, 150, 153, 156, 164, 168, 171, 172, 188, 192, 198, 204, 207, 212, 220, 228, 234, 236, 244, 260, 261, 264, 268, 272, 276, 279, 284, 292, 294, 306, 308, 312, 315, 316, 325, 332, 333, 340, 342, 348, 350

Offset: 1

Antti Karttunen, Jul 28 2020

nonn

Numbers k such that either A336551(k) and A326143(k) are both zero (in which case k is squarefree), or A336551(k) divides A326143(k) (in which case k is not squarefree).

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A007947, A326143, A336550, A336551, A336553 (odd terms).

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); };
isA336552(n) = { my(u=A336551(n)); (u==gcd(u,A326143(n))); };

A336554 Odd numbers k such that rad(k) divides sigma(k).

Original entry on oeis.org

1, 135, 891, 1521, 3375, 5733, 10935, 11907, 41067, 43875, 84375, 89667, 92781, 98865, 107811, 108927, 154791, 185625, 200655, 216513, 226233, 273375, 274625, 287469, 307125, 336141, 416745, 448335, 480249, 544635, 557375, 570375, 590625, 627669, 628849, 648675, 692055, 823875, 885735, 931095, 968877, 1071875, 1108809, 1131165

Offset: 1

Antti Karttunen, Jul 28 2020

nonn

Only a minority of terms seem to be also in A228058: 5733, 92781, 2069613, 3341637, 4179357, 5929605, 60998353, 67637349, 89162541 among the first 216, the five of them which occur also in A263983.

Question: Is the intersection with A336553 empty?

Amiram Eldar, Table of n, a(n) for n = 1..1200 (terms 1..216 from Antti Karttunen)
Index entries for sequences where odd perfect numbers must occur, if they exist at all.

Odd terms of A175200.
Cf. A000203, A007947, A228058, A263983.
Cf. also A336553.

isA336554(n) = if(!(n%2),0,!(sigma(n) % factorback(factorint(n)[, 1])));

cp's OEIS Frontend

A336552 Numbers k such that A003557(k)-1 either divides A326143(k) [= A001065(k) - A007947(k)], or both are zero. Numbers k such that gcd(A336551(k), A326143(k)) is equal to A336551(k).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI