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

Offset: 1

Author

Antti Karttunen, Jul 21 2025

Keywords

• nonn
• more

Comments

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

If it exists, a(15) > 2^30 (1073741824).

Links

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

Crossrefs

Subsequence of A353679.

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

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

Programs

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)