A388265 Numbers k for which gcd(A276086(sigma(k)-k), A276086(k)) is equal to A276086(k), where A276086 is the primorial base exp-function, and sigma is the sum of divisors function.

6, 12, 18, 20, 28, 30, 36, 42, 60, 66, 90, 96, 102, 104, 108, 126, 132, 162, 186, 196, 210, 216, 222, 240, 246, 252, 260, 272, 276, 282, 288, 300, 304, 306, 312, 360, 366, 368, 390, 402, 420, 426, 432, 448, 450, 456, 464, 468, 480, 486, 496, 500, 510, 546, 572, 582, 588, 606, 630, 636, 642, 648, 650, 660, 666, 672

Offset

1,1

Comments

Numbers k such that in the primorial base expansion (A049345) of sigma(k)-k [= A001065(k)] all digits are greater than or equal to the corresponding digits in the primorial base expansion of k.

This sequence is loosely analogous to the sequence A324649, 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 | A388264(k) = A276086(k)}.

Example

For k = 272, A001065(272) = sigma(272)-272 = 286, with A049345(286) = 12220 and A049345(272) = 12010. All digits in the latter are <= of the corresponding digits in the former, therefore 272 is included in this sequence.

Prog

(PARI) is_A388265(n) = { my(s=sigma(n), p=2); s -= n; 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, A001065, A049345, A276086, A379493, A388264.

Subsequence of A023196.

Subsequences: A000396, A388266 (primitive terms), A388267 (odd terms).

Cf. also A324649, A388271, A388034, A388036.

Sequence in context: A228870 A291022 A348719 * A388028 A316221 A138939

Adjacent sequences: A388262 A388263 A388264 * A388266 A388267 A388268

Keyword

nonn

Author

Antti Karttunen, Sep 16 2025

Status

approved