A354194 Numbers k for which phi(A267099(k)) is equal to phi(k), but the number of 4m+1 and 4m+3 primes in the prime factorization of k (when counted with multiplicity) is not equal. Here A267099 is fully multiplicative involution swapping the positions of 4m+1 and 4m+3 primes, and phi is Euler totient function.

69037, 70807, 76635, 79577, 81631, 82425, 88335, 95025, 138074, 141614, 149209, 153270, 153703, 159154, 163262, 164850, 171989, 176670, 177199, 190050, 276148, 283228, 298418, 306540, 307406, 318308, 326524, 329700, 343978, 353340, 354398, 380100, 552296, 566456, 596836, 613080, 614812, 636616, 653048, 659400, 687956

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..377

Example

A354102(69037) = phi(A267099(69037)) = phi(70807) = phi(69037) = 62400, and 69037 = 17*31*131, therefore 69037 is included in this sequence, and likewise is 70807 = 11*41*157.

Prog

(PARI)
A354188(n) = (eulerphi(A267099(n)) == eulerphi(n)); \\ Uses the program given in A267099.
A342025(n) = {my(f = factor(n)); sum(k=1, #f~, ((f[k, 1] % 4)==1)*f[k, 2]) == sum(k=1, #f~, ((f[k, 1] % 4)==3)*f[k, 2]); }; \\ From isok function in A072202
isA354194(n) = (A354188(n) && !A342025(n));

Crossrefs

Setwise difference A354189 \ A072202.

Cf. A002144, A002145, A342025, A354188.

Sequence in context: A046516 A199997 A250500 * A096551 A096552 A031663

Adjacent sequences: A354191 A354192 A354193 * A354195 A354196 A354197

Keyword

nonn

Author

Antti Karttunen, May 20 2022

Status

approved