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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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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.
Sequence in context: A046516 A199997 A250500 * A096551 A096552 A031663
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 20 2022
STATUS
approved

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Last modified May 29 14:24 EDT 2024. Contains 372952 sequences. (Running on oeis4.)