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

Author

Antti Karttunen, May 20 2022

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Setwise difference A354189 \ A072202.

Cf. A002144, A002145, A342025, A354188.

Programs

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));