A063534 Numbers k such that C(k) = H(k) + d(k), where C(k) is Chowla's function A048050, H(k) is the half-totient function A023022 and d(k) is the number of divisors function A000005.

6, 8, 15, 21, 33, 39, 51, 57, 69, 87, 93, 111, 123, 129, 141, 159, 177, 183, 201, 213, 219, 237, 249, 267, 291, 303, 309, 321, 327, 339, 381, 393, 411, 417, 447, 453, 471, 489, 501, 519, 537, 543, 573, 579, 591, 597, 633, 669, 681, 687, 699, 717, 723, 753

Offset

1,1

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Formula

Conjecture: a(n) = A001748(n), n <> 2. - R. J. Mathar, Dec 15 2008

The conjecture is false. The least counterexample is a(11546) = 368335 = 5 * 11 * 37 * 181. The next counterexample is 4922335, and there are no more below 10^10. - Amiram Eldar, Apr 15 2024

Mathematica

Select[Range[1000], DivisorSigma[1, #] - 1 - # == EulerPhi[#]/2 + DivisorSigma[0, #] &] (* Paolo Xausa, Apr 17 2024 *)

Prog

(PARI) C(n)=sigma(n)-n-1;
H(n)=eulerphi(n)/2;
j=[]; for(n=1, 1200, if(C(n)==H(n)+numdiv(n), j=concat(j, n))); j
(PARI) { n=0; for (m=1, 10^9, if (sigma(m) - m - 1 == eulerphi(m)/2 + numdiv(m), write("b063534.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 25 2009
(PARI) is(n) = {my(f = factor(n)); sigma(f) - n - 1 == eulerphi(f) / 2 + numdiv(f); } \\ Amiram Eldar, Apr 15 2024

Crossrefs

Cf. A048050, A023022, A000005, A001748.

Sequence in context: A357358 A315925 A315926 * A361420 A162651 A275321

Adjacent sequences: A063531 A063532 A063533 * A063535 A063536 A063537

Keyword

easy,nonn,changed

Author

Jason Earls, Aug 02 2001

Status

approved