A334021 -id:A334021 - cp's OEIS frontend

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

Amiram Eldar, May 10 2024

nonn

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

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

Subsequence of A070258 and A372693.

Cf. A334021, A324310, A372692.

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] &]

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);}

A334022 Numbers k such that s(k) = s(k+1) = s(k+2) = s(k+3), where s(k) is the sum of unitary divisors of k that are smaller than sqrt(k) (A334019).

Original entry on oeis.org

2, 46351754, 102841142, 158071592, 667930085, 851043553, 1097409992, 1580045430, 1595193655, 1698842487, 1919035496, 1951958341, 2279249234, 2507918727, 2520080695, 2741951910, 3335769314, 3654512455, 3713106152, 4209598844, 4351540982, 4369408604, 4480814965

Offset: 1

Amiram Eldar, Apr 12 2020

nonn

			2 is a term since A334019(2) = A334019(3) = A334019(4) = 1.

Cf. A325175, A334019, A334020, A334021.

s[n_] := DivisorSum[n, # &, #^2 < n && CoprimeQ[#, n/#] &]; seq={}; s1 = s[1]; s2 = s[2]; s3 = s[3]; Do[s4 = s[n]; If[s1 == s2 && s2 == s3 && s3 == s4, AppendTo[seq, n - 3]]; s1 = s2; s2 = s3; s3 = s4, {n, 4, 10^9}]; seq

cp's OEIS Frontend

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

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