A388036 Numbers k such that gcd(A276086(sigma(k)), A276086(3*k)) = A276086(3*k), where A276086 is the primorial base exp-function, and sigma is the sum of divisors function.

120, 180, 240, 360, 420, 600, 660, 672, 780, 840, 1200, 1260, 1344, 1620, 1680, 1800, 1890, 2040, 2352, 2772, 3120, 3150, 3240, 3300, 3720, 3900, 4032, 4080, 4140, 4284, 4410, 4620, 4704, 4800, 4860, 5400, 5460, 5616, 5670, 5700, 5760, 5880, 6240, 6300, 6600, 6660, 6930, 7080, 7140, 7200, 7920, 7980, 8160, 8760

Offset

1,1

Comments

Numbers k such that in the primorial base expansion (A049345) of sigma(k) all digits are greater than or equal to the corresponding digits in the primorial base expansion of 3*k. This sequence is loosely analogous to the sequence A388022, but uses primorial base instead of base-2.

Links

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

Index entries for sequences related to primorial base.

Index entries for sequences related to sigma(n).

Formula

{k | A388033(k) = A276086(3*k)}.

Example

For k = 2772, sigma(2772) = 8736, with A049345(8736) = 384100 and A049345(3*2772) = 364100. All the digits in the latter are <= of the digits in the former, therefore 2772 is included in this sequence.

Prog

(PARI) is_A388036(n) = { my(s=sigma(n), p=2); n *= 3; while(n, if(min(n%p, s%p) != (n%p), return(0)); n = n\p; s = s\p; p = nextprime(1+p)); (1); };

Crossrefs

Cf. A000203, A049345, A276086, A388031, A388033.

Subsequence of A023197.

Subsequences: A005820, A388037 (primitive terms).

Cf. also A388022, A388034, A388271.

Sequence in context: A023197 A204828 A204830 * A279088 A388024 A337479

Adjacent sequences: A388033 A388034 A388035 * A388037 A388038 A388039

Keyword

nonn,base

Author

Antti Karttunen, Sep 16 2025

Status

approved