A353635 Numbers k such that phi(k) = phi(sigma(k)) and A003958(k) = A003958(sigma(k)).

1, 26, 74, 122, 146, 314, 386, 554, 626, 794, 842, 914, 1082, 1226, 1322, 1346, 1466, 1514, 1754, 1994, 2186, 2306, 2402, 2426, 2474, 2642, 2762, 2906, 3242, 3314, 3506, 3746, 3866, 3986, 4034, 4274, 4682, 4946, 5114, 5186, 5594, 5714, 5834, 6122, 6434, 6506, 6626, 7034, 7466, 8042, 8114, 8354, 8522, 8546, 8714, 8882

Offset: 1

Author

Antti Karttunen, May 04 2022

Keywords

• nonn

Comments

Question 1: Are there any odd terms after the initial 1?

Interestingly, most of the terms seem to belong to a set where the abundancy index (ratio sigma(n)/n) converges towards 3/2. But there are exceptions, see A353634 for example.

Links

• Index entries for sequences where odd perfect numbers must occur, if they exist at all
• Index entries for sequences related to sigma(n)

Crossrefs

Intersection of A006872 and A351446. A353634 lists the nondeficient terms.

Cf. A000010, A000203, A003958, A062401, A351440, A351442.

Programs

PARI

A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
isA353635(n) = { my(s=sigma(n)); ((eulerphi(s)==eulerphi(n)) && (A003958(s)==A003958(n))); };