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

1215, 98415, 273375, 413343, 846368

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..5.

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. A072066, A005179, A037019.

Sequence in context: A130680 A346207 A068783 * A235889 A321062 A059287

Adjacent sequences: A331622 A331623 A331624 * A331626 A331627 A331628

Keyword

nonn,hard,more

Author

Jianing Song, Jan 22 2020

Status

approved