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A067598 Decimal encoding of the prime factorization of n is a multiple of n. 3
21, 36, 8277, 22987, 31199, 59577, 2092101, 25224589, 29963201, 564423629, 1353149983, 30011570617, 37090609821, 392629311959 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If n = p_1^e_1 * ... * p_r^e_r with p_1 < ... < p_r, then the decimal encoding is p_1 e_1...p_r e_r. For example, 15 = 3^1 * 5^1, so has decimal encoding 3151.

a(12) > 10^10. [From Donovan Johnson, Mar 26 2010]

a(15) > 10^12. - Giovanni Resta, Aug 17 2016

LINKS

Table of n, a(n) for n=1..14.

EXAMPLE

The prime factorization of 21 = 3^1 * 7^1 with corresponding encoding 3171. 3171 = 21 * 151, a multiple of 21. So 21 is a term of the sequence.

MATHEMATICA

Select[Range[100000], Mod[FromDigits[Flatten[IntegerDigits /@ Flatten[FactorInteger[ # ]]]], # ] ==0 &]

PROG

(PARI) {a067598(a, b) = local(n, v); for(n=max(2, a), b, v=factor(n); if(eval(concat(vector(matsize(v)[1], k, concat(vector(matsize(v)[2], j, Str(v[k, j]))))))%n==0, print1(n, ", ")))}

CROSSREFS

Sequence in context: A112352 A298472 A168513 * A043683 A173589 A043572

Adjacent sequences:  A067595 A067596 A067597 * A067599 A067600 A067601

KEYWORD

base,easy,nonn

AUTHOR

Joseph L. Pe, Jan 31 2002

EXTENSIONS

Edited and extended by Robert G. Wilson v, Feb 02 2002

Two more terms from Klaus Brockhaus, Feb 20 2002

a(10)-a(11) from Donovan Johnson, Mar 26 2010

a(12)-a(14) from Giovanni Resta, Aug 17 2016

STATUS

approved

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Last modified November 18 17:33 EST 2019. Contains 329287 sequences. (Running on oeis4.)