A386420 Odd numbers k that are closer to being perfect than previous terms and also satisfy the conditions that sigma(k) preserves the 3-adic valuation of k, and that sigma(k) == -k (mod 3).

7, 15, 105, 495, 1365, 2205, 9405, 26145, 31815, 497835, 654675, 1984455, 7188885, 9018009, 9338595, 9958905, 13777785, 13800465, 14571585, 47020995, 78867495, 132884115, 210124665, 363860775

Offset: 1

Author

Antti Karttunen, Jul 21 2025

Keywords

• nonn
• more

Comments

Question: Is 2205 the only term also in A228058?

If it exists, a(25) > 1275068416.

Links

• Index entries for sequences where (the least) odd perfect number must occur

Crossrefs

Subsequence of A349752, thus also of A349749 and of A349751.

Cf. A000203.

Cf. also A171929, A228059, A386419, A386421, A386422.

Programs

PARI

isA349752(n) = if(!(n%2), 0, my(s=sigma(n)); (0==(s+n)%3) && valuation(s, 3)==valuation(n, 3));
m=-1; n=0; k=0; while(m!=0, n++; if(!(n%(2^25)),print1("("n")")); if(isA349752(n), if((m<0) || abs((sigma(n)/n)-2)