A387165 Nondeficient numbers k for which A324644(k)/A324198(k) = 2.

38745, 77805, 78435, 118755, 141075, 157815, 210735, 237195, 241605, 294975, 300105, 323505, 364455, 371925, 390195, 409185, 455715, 475335, 499905, 567945, 607635, 660825, 701415, 733005, 766395, 806085, 809325, 872235, 885465, 891135, 937755, 964845, 978705, 1101555, 1150065, 1201095, 1229445, 1265355, 1293705

Offset

1,1

Comments

First three nonmultiples of 5 occur at a(138), a(276), a(356) = 4446981, 8909901, 11234223. (Cf. A005231, A064001).

First term that is also a term of A228058 (and of A229125) is a(16855) = 666996525. See also A386430, A387160.

Odd nonsquare nondeficient numbers such that when x = A276086(n), then for all odd primes p, min(v_p(x), v_p(sigma(n))) is equal to min(v_p(x), v_p(n)), where v_p(.) stands for the p-adic valuation. Thus, either p^e||n and p^e||sigma(n) when v_p(x) >= e, or v_p(x) <= v_p(n) and v_p(x) <= v_p(sigma(n)). - Antti Karttunen, Sep 18 2025

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).

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

Formula

{k | sigma(k) >= 2*k, A324644(k) = 2*A324198(k)}.

Prog

(PARI)
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
is_A387165(n) = if(sigma(n)<2*n, 0, my(u=A276086(n)); (gcd(sigma(n), u)==2*gcd(n, u)));
(PARI) is_A387165(n) = if(sigma(n)<2*n, 0, my(p=2, s=sigma(n), x=n, vnp, vsp); while(x, vnp = valuation(n, p); vsp = valuation(s, p); if(min((x%p), vsp) != (2==p)+min((x%p), vnp), return(0)); x = x\p; p = nextprime(1+p)); (1)); \\ Antti Karttunen, Sep 17 2025

Crossrefs

Intersection of A023196 and A364286. Subsequence of A088828.

Cf. A000203, A228058, A229125, A276086.

Cf. also A371082, A386422, A387163 and A047802, A064001, A115414, A386430, A387160.

Sequence in context: A043666 A180462 A185851 * A154062 A204759 A206597

Adjacent sequences: A387162 A387163 A387164 * A387166 A387167 A387168

Keyword

nonn,base

Author

Antti Karttunen, Aug 28 2025

Status

approved