A386419 Odd numbers k that are closer to being perfect than previous terms, and also satisfy the condition that phi(k) = phi(sigma(k)).

1, 3, 15, 45, 585, 2295, 11475, 29835, 72675, 424575, 7977165, 28851975, 29277885, 39317175, 2359730475, 2708065305

Offset

1,2

Comments

Questions: Is 45 the only term also in A228058? (See also A354362). Are there only multiples of 5 after the two initial terms?

Links

Table of n, a(n) for n=1..16.

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

Example

From David A. Corneth, Feb 09 2026: (Start)
1 is in the sequence which sets the record closest to perfect to abs(sigma(1)/1-2) = 1 and phi(1) = phi(sigma(1)).
2 is not in the sequence as 1 = phi(2) != phi(sigma(2)) = phi(3) = 2.
3 is in the sequence which sets the record closest to perfect to abs(sigma(3)/3-2) = 2/3 and phi(3) = phi(sigma(3)). (End)

Prog

(PARI)
A353680(n) = ((n%2) && (eulerphi(sigma(n))==eulerphi(n)));
isA353679(n) = A353680(n);
m=-1; n=0; k=0; while(m!=0, n++; if(!(n%(2^25)), print1("("n")")); if(isA353679(n), if((m<0) || abs((sigma(n)/n)-2)<m, m=abs((sigma(n)/n)-2); k++; write("b386419.txt", k, " ", n); print1(n, ", "))));

Crossrefs

Subsequence of A353679.

Cf. A000010, A000203, A000396, A228058, A354362.

Cf. also A171929, A228059, A386420, A386421, A386422.

Sequence in context: A110464 A261505 A331505 * A088108 A226030 A232077

Adjacent sequences: A386416 A386417 A386418 * A386420 A386421 A386422

Keyword

nonn,more

Author

Antti Karttunen, Jul 21 2025

Extensions

a(16) from Alexander Violette confirmed and a(15) added by Max Alekseyev, Feb 09 2026

Status

approved