A342654 a(n) = A005940(1+A324104(n)); Euler totient phi conjugated by A156552.

1, 2, 2, 3, 3, 5, 5, 9, 3, 9, 7, 15, 11, 11, 5, 7, 13, 25, 17, 21, 9, 35, 19, 45, 5, 121, 9, 49, 23, 25, 29, 81, 11, 385, 7, 21, 31, 23, 35, 49, 37, 55, 41, 39, 15, 1105, 43, 135, 7, 35, 121, 51, 47, 125, 25, 99, 385, 4693, 53, 105, 59, 85085, 21, 55, 13, 175, 61, 5929, 23, 77, 67, 77, 71, 279841, 25, 8281, 11, 1225

Offset

1,2

Links

Table of n, a(n) for n=1..78.

Index entries for sequences computed from indices in prime factorization

Formula

a(1) = 1, and for n > 1, a(n) = A005940(1+A000010(A156552(n))).

a(n) = A005940(1+A324104(n)).

For n >= 2, a(A000040(n)) = A000040(n-1).

Prog

(PARI)
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res};
A324104(n) = if(1==n, 0, eulerphi(A156552(n)));
A342654(n) = A005940(1+A324104(n));

Crossrefs

Cf. A000010, A005940, A156552, A324104.

Cf. also A332223 (sigma similarly conjugated).

Sequence in context: A246998 A000358 A032244 * A166588 A277321 A262365

Adjacent sequences: A342651 A342652 A342653 * A342655 A342656 A342657

Keyword

nonn

Author

Antti Karttunen, Mar 18 2021

Status

approved