A360527 - OEIS

A360527

Numbers k such that A360522(k) = A360522(k+1).

4, 8, 14, 176, 895, 956, 957, 1334, 1634, 1724, 1725, 1844, 1934, 2685, 2871, 3404, 3759, 4047, 4136, 5175, 7004, 7315, 7599, 8055, 12104, 13760, 18415, 20145, 29392, 32944, 33998, 42818, 44095, 44516, 49599, 60356, 74918, 79826, 79833, 84134, 85172, 85744, 86343

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OFFSET

1,1

COMMENTS

Numbers k such that A360522(k) = A360522(k+1) = A360522(k+2) exist: 956 and 1724. Are there any other terms like these? There are none below 1.8*10^10.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..2500

EXAMPLE

4 is a term since A360522(4) = A360522(5) = 6.

MATHEMATICA

f[p_, e_] := p^e + e; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Position[Partition[Array[s, 10^5], 2, 1], _?(SameQ @@ # &)] // Flatten

PROG

(PARI) s(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^f[i, 2] + f[i, 2]); }

lista(nmax) = {my(s1 = s(1), s2); for(n=2, nmax, s2=s(n); if(s1 == s2, print1(n-1, ", ")); s1 = s2); }

CROSSREFS

Cf. A360522.

Similar sequences: A002961, A064115, A064125, A293183, A306985.