A331625 Numbers k such that both k and k+1 are exceptional (A072066).

1215, 98415, 273375, 413343, 846368, 1987983, 2302911, 6082047, 6200144, 8089712, 9034496, 9861183, 11868848, 13010463, 13325391, 13955247, 16159743, 16592768, 17537552, 18482336, 20686832, 20883663, 21198591, 22143375, 22891328, 23206256, 24347871, 25607583

Offset

1,1

Comments

Conjecture: for every p > 0, there exist infinitely many k such that k, k+1, ..., k+p-1 are all exceptional numbers. In specific, there exist infinitely many k such that both k and k+1 are exceptional.

Links

Table of n, a(n) for n=1..28.

Example

1215 = 3^5 * 5, 1216 = 2^6 * 19;
thus A037019(1215) = 2^4 * 3^2 * 5^2 * 7^2 * 11^2 * 13^2 = 3607203600, A037016(1216) = 2^18 * 3 * 5 * 7 * 11 * 13 * 17 = 66913566720;
but the smallest number with 1215 divisors is 3073593600 = 2^8 * 3^4 * 5^2 * 7^2 * 11^2, the smallest number with 1216 divisors is 35424829440 = 2^18 * 3^3 * 5 * 7 * 11 * 13;
so both 1215 and 1216 are exceptional, so 1215 is a term.

Prog

(PARI) isA331625(n) = A037019(n+1) > A005179(n+1) && A037019(n) > A005179(n) \\ See A037019 and A005179 for their programs. Warning: this is extremely inefficient

Crossrefs

Cf. A005179, A037019, A072066.

Sequence in context: A130680 A346207 A068783 * A235889 A321062 A059287

Adjacent sequences: A331622 A331623 A331624 * A331626 A331627 A331628

Keyword

nonn

Author

Jianing Song, Jan 22 2020

Extensions

More terms from Jinyuan Wang, Jan 21 2025

Status

approved