A340077 Odd numbers k for which k-1 is a multiple of A053575(k) [the odd part of phi(k)].

1, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29, 31, 37, 41, 43, 47, 51, 53, 59, 61, 67, 71, 73, 79, 83, 85, 89, 91, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 255, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313

Offset

1,2

Comments

Sequence A003961(A340076(i)), i = 1.., sorted into ascending order. In other words, this sequence consists of such odd numbers k that A064989(k) is in A340076.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Mathematica

q[k_] := OddQ[k] && Divisible[k-1, (# / 2^IntegerExponent[#, 2])& @ EulerPhi[k]]; Select[Range[320], q] (* Amiram Eldar, Mar 30 2026 *)

Prog

(PARI)
A000265(n) = (n>>valuation(n, 2));
isA340077(n) = ((n%2)&&!((n-1)%A000265(eulerphi(n))));
(PARI)
A064989(n) = { my(f=factor(n)); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f) };
isA340077(n) = ((n%2)&&(1==A340075(A064989(n)))); \\ Needs also code from A340075.

Crossrefs

Cf. A064989, A340075, A340076.

Subsequence of A339879.

Subsequences: A065091, A339880 (composite terms), A339869, A339870 (and their further subsequences).

Sequence in context: A302568 A359260 A294674 * A179458 A062086 A283680

Adjacent sequences: A340074 A340075 A340076 * A340078 A340079 A340080

Keyword

nonn

Author

Antti Karttunen, Dec 29 2020

Status

approved