A392184 - OEIS

A392184

a(n) is the least k for which omega(k)*omega(k + 1)*omega(k + 2) = n where omega = A001221, or -1 if no such k exists.

1, 2, 4, 29, 10, 2309, 28, 1138829, 20, 130, 2308, 239378649509, 68, 461282657605769, 570569, 2728, 208, 3338236629672919864889, 154, 11465419967969569966774409, 3568, 570568, 200560490129, 447252622660353534197972753024069, 713, 77140, 304250263527208, 644

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OFFSET

0,2

LINKS

Sean A. Irvine, Table of n, a(n) for n = 0..43

Brian Hayes, Does having prime neighbors make you more composite?, Bit-Player Article, Nov 04 2021.

FORMULA

From Vaclav Kotesovec, Jan 03 2026: (Start)

For p>2 prime, A002110(p) - 1 <= a(p) <= A075590(p) - 1.

Conjecture: a(p) = A075590(p) - 1. (End)

EXAMPLE

k | omega(k)*omega(k + 1)*omega(k + 2) = n

-----------------------------------------------------------

1 | 0 * 1 * 1 = 0

2 | 1 * 1 * 1 = 1

4 | 1 * 1 * 2 = 2

29 | 1 * 3 * 1 = 3

10 | 2 * 1 * 2 = 4

2309 | 1 * 5 * 1 = 5

28 | 2 * 1 * 3 = 6

1138829 | 1 * 7 * 1 = 7

20 | 2 * 2 * 2 = 8

130 | 3 * 1 * 3 = 9

2308 | 2 * 1 * 5 = 10

PROG

(Magma) [Min([k: k in [1..10000] | #PrimeDivisors(k)*#PrimeDivisors(k+1)*#PrimeDivisors(k+2) eq n]): n in [0..6]];

(PARI) isok(k, n) = omega(k)*omega(k+1)*omega(k+2) == n;

a(n) = my(k=1); while (! isok(k, n), k++); k; \\ Michel Marcus, Feb 26 2026

CROSSREFS

Cf. A001221, A002110, A075590, A391216, A006549, A088071, A173037, A264734, A329364, A392232, A393108.

Sequence in context: A329102 A126580 A329063 * A124687 A267122 A018291

Adjacent sequences: A392181 A392182 A392183 * A392185 A392186 A392187

KEYWORD

nonn,more

AUTHOR

Juri-Stepan Gerasimov, Jan 02 2026

EXTENSIONS

a(11)-a(18) from Vaclav Kotesovec, Jan 03 2026

STATUS

approved