A046397 Palindromes which are the product of exactly 7 distinct primes.

22444422, 24266242, 26588562, 35888853, 36399363, 43777734, 47199174, 51066015, 53588535, 53888835, 55233255, 59911995, 60066006, 62588526, 62700726, 62888826, 81699618, 87788778, 89433498, 122434221, 202040202

Offset: 1

Author

Patrick De Geest, Jun 15 1998

Keywords

• nonn
• base

Comments

The original name "Palindromes with exactly 7 distinct prime factors" did not exclude that one or more of the factors occurred to a higher power: this is sequence A373467. As the listed data show, terms of this sequence must be squarefree. - M. F. Hasler, Jun 06 2024

Examples

			The first two palindromes with 7 distinct prime factors are 20522502 = 2 * 3^2 * 7 * 11 * 13 * 17 * 67 and 21033012 = 2^2 * 3 * 7 * 11 * 13 * 17 * 103, but these are excluded since one of the prime factors occurs to a higher power.
a(1) = 22444422 = 2 * 3 * 7 * 11 * 13 * 37 * 101, which is squarefree, is therefore the first term of this sequence.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A046333 (similar but prime factors counted with multiplicity), A373467 (similar but counting just the distinct prime divisors).

Cf. A002113 (palindromes), A123321 (products of 7 distinct primes), A176655 (numbers with omega = 7 distinct prime divisors).

Programs

Maple

digrev:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
filter:= proc(n) local F;
  F:= ifactors(n)[2];
  nops(F) = 7 and map(t -> t[2],F)=[1$7]
end proc:
Res:= NULL:
count:= 0:
for d from 2  while count < 100 do
  if d::even then
    m:= d/2;
    for n from 10^(m-1) to 10^m-1 while count < 100 do
      v:= n*10^m+digrev(n);
      if filter(v) then count:= count+1; Res:= Res, v; fi;
    od;
  else
    m:= (d-1)/2;
    for n from 10^(m-1) to 10^m-1 while count < 100 do
      for y from 0 to 9 while count < 100 do
         v:= n*10^(m+1)+y*10^m+digrev(n);
         if filter(v) then count:= count+1; Res:= Res, v; fi;
    od od
  fi
od:
Res; # Robert Israel, Jan 20 2020

PARI

A046397_upto(N, start=vecprod(primes(7)), num_fact=7)={ my(L=List()); is_A002113(start)&& start--; while(N >= start = nxt_A002113(start), omega(start)==num_fact && issquarefree(start) && listput(L, start)); L} \\ M. F. Hasler, Jun 06 2024