A372694 Numbers k such that A372692(k) = A372692(k+1) = A372692(k+2) > 1.

17784450, 28873348, 38990474, 44534923, 48780675, 85648274, 95438475, 100982924, 111100050, 157757850, 184508323, 188754075, 225621674, 240956324, 251073450, 308820148, 318937274, 334271924, 365595074, 371139523, 378806848, 391046850, 437704650, 505568474, 511112923

Offset: 1

Author

Amiram Eldar, May 10 2024

Keywords

• nonn

Comments

Can 4 consecutive integers have the same value of A372692? There are none below 2*10^10.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1200

Crossrefs

Subsequence of A070258 and A372693.

Cf. A334021, A324310, A372692.

Programs

Mathematica

f[p_, e_] := p^(2^(-1 + Position[Reverse@ IntegerDigits[e, 2], ?(# == 0 &)])); s[1] = 1; s[n] := s[n] = Times @@ (Flatten@ (f @@@ FactorInteger[n]) + 1);
Select[Range[10^8], (s1 = s[#]) > 1 && s1 == s[# + 1] == s[# + 2] &]

PARI

s(n) = {my(f = factor(n), k); prod(i = 1, #f~, k = apply(x -> 1 - x, binary(f[i, 2])); prod(j = 1, #k, if(k[j], f[i, 1]^(2^(#k-j)) + 1, 1)));}
lista(kmax) = {my(s1 = s(1), s2 = s(2), s3); for(k = 3, kmax, s3 = s(k); if(s1 > 1 && s1 == s2 && s2 == s3, print1(k - 2, ", ")); s1 = s2; s2 = s3);}