A251362 -id:A251362 - cp's OEIS frontend

A251360 Numbers k such that k is the concatenation of prime factors of pi(k), in increasing order.

1117, 2163, 2537, 5137, 222926801

Offset: 1

Jahangeer Kholdi, Dec 01 2014

Numbers k such that k = A037276(A000720(k)).
Conjecture: numbers k such that k = A084317(A000720(k)). - Chai Wah Wu, Apr 04 2018
a(6) > 10^12 if exists. - Max Alekseyev, May 16 2025

			1117 is in the sequence since pi(1117) = 11*17,
2163 is in the sequence since pi(2163) = 2*163,
2537 is in the sequence since pi(2537) = 2*5*37,
and 5137 is in the sequence since pi(5137) = 5*137.

Chris Caldwell, G. L. Honaker and Lewis, 1117

Cf. A000040, A000720, A251361, A251362.

a251360[n_Integer] := Select[Range[n], # == FromDigits[Flatten@IntegerDigits[First@ Transpose@ FactorInteger[PrimePi[#]]]] &]; a251360[10^5] (* Michael De Vlieger, Dec 03 2014 *)

from sympy import prime, factorint
A251360_list, p = [], 3
for n in range(2,10**6):
    q, fn = prime(n+1), factorint(n)
    m = int(''.join(str(d)*fn[d] for d in sorted(fn)))
    if p <= m < q:
        A251360_list.append(m)
    p = q # Chai Wah Wu, Dec 10 2014, corrected Apr 04 2018

a(5) from Chai Wah Wu, Dec 10 2014

A251363 Numbers n such that n is the concatenation of distinct prime factors of phi(n), in decreasing order.

Original entry on oeis.org

237532, 832332, 82953292, 423238803752

Offset: 1

Jahangeer Kholdi, Dec 03 2014

Numbers n such that n = A085307(A000010(n)). - Michel Marcus, Dec 06 2014

			237532 is in the sequence since phi(237532)=23*7*5*3^2*2^4,
832332 is in the sequence since phi(832332)=83*23*3^2*2^4, and
82953292 is in the sequence since phi(82953292)=829*53*29*2^5.

Cf. A000010, A000040, A085307, A251360, A251361, A251362.

a251363[n_Integer] :=
Rest@ Select[Range[n], # == FromDigits[Flatten@ IntegerDigits[
Sort[First@ Transpose@ FactorInteger[EulerPhi[#]], Greater]]] &]; a251363[10^6] (* Michael De Vlieger, Dec 03 2014 *)

a(4) from Max Alekseyev, Feb 10 2025

cp's OEIS Frontend

A251360 Numbers k such that k is the concatenation of prime factors of pi(k), in increasing order.

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