A388028 Numbers k for which A003961(k) > 2*k and A003961(k)-2*k OR A003961(k)-sigma(k) = A003961(k)-2*k, where OR is bitwise-or (A003986), and A003961 is fully multiplicative with a(p) = nextprime(p).

6, 12, 18, 20, 28, 30, 56, 66, 88, 96, 100, 104, 112, 126, 138, 176, 180, 210, 220, 258, 264, 280, 348, 354, 364, 368, 372, 390, 444, 464, 496, 532, 560, 582, 606, 642, 650, 672, 700, 744, 748, 774, 836, 860, 894, 896, 906, 984, 1002, 1158, 1182, 1188, 1216, 1220, 1232, 1248, 1266, 1352, 1360, 1376, 1422, 1430, 1484

Offset

1,1

Comments

Equally, numbers k for which A003961(k) > 2*k and A003961(k)-2*k AND A003961(k)-sigma(k) = A003961(k)-sigma(k), where AND is bitwise-and, A004198.

Links

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

Index entries for sequences computed from indices in prime factorization.

Index entries for sequences related to binary expansion of n.

Index entries for sequences related to sigma(n).

Formula

{k | A252748(k) > 0, A003986(A252748(k), A286385(k)) == A252748(k)}.

Prog

(PARI)
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f);
is_A388028(n) = { my(u=A003961(n)); ((u > 2*n) && bitor(u-2*n, u-sigma(n))==(u-2*n)); };
(PARI) is_A388028(n) = { my(u=A003961(n), s=sigma(n)); ((u > 2*n) && bitand(u-2*n, u-s)==(u-s)); }; \\ Alternatively.

Crossrefs

Cf. A000203, A003986, A003961, A004198, A252748, A286385.

Subsequence of A023196, which is a subsequence of A246282.

Subsequences: A000396, A388029 (odd terms), A388030 (primitive terms).

Cf. also A324652, A324726, A326134.

Sequence in context: A291022 A348719 A388265 * A316221 A138939 A221220

Adjacent sequences: A388025 A388026 A388027 * A388029 A388030 A388031

Keyword

nonn

Author

Antti Karttunen, Sep 15 2025

Status

approved