A388029 Odd 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).

2205, 3465, 8415, 12285, 18585, 28035, 44415, 66885, 92565, 100035, 102375, 222915, 236925, 314685, 327915, 374535, 394065, 427455, 442365, 517725, 532875, 697515, 810495, 865725, 898425, 928305, 947625, 967575, 1029735, 1055925, 1121715, 1247085, 1349775, 1360485, 1537305, 1593405, 1605555, 1606605, 1670625, 1924335

Offset

1,1

Comments

Equally, odd 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.

The first non-multiple of 5 occurs as a(71) = 5806647.

Links

Antti Karttunen, Table of n, a(n) for n = 1..1026

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).

Index entries for sequences where odd perfect numbers must occur, if they exist at all.

Formula

{k | k odd, 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_A388029(n) = if(!(n%2), 0, my(u=A003961(n)); ((u > 2*n) && bitor(u-2*n, u-sigma(n))==(u-2*n)));

Crossrefs

Odd terms of A388028.

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

Sequence in context: A075455 A233444 A125015 * A386427 A348743 A252397

Adjacent sequences: A388026 A388027 A388028 * A388030 A388031 A388032

Keyword

nonn

Author

Antti Karttunen, Sep 15 2025

Status

approved