A358174 Smaller of a pair of numbers (m, m+1) such that both are products P of composite prime powers with omega(P) > 1.

675, 9800, 235224, 465124, 1825200, 11309768, 384199200, 592192224, 4931691075, 5425069447, 13051463048, 221322261600, 865363202000, 8192480787000, 11968683934831, 13325427460800, 15061377048200, 28821995554247, 48689748233307, 511643454094368, 1558709801289000

Offset

1,1

Comments

a(n) = A286708(k), where k is a position of 1 in A358173.

Links

Table of n, a(n) for n=1..21.

Example

a(1) = 675, since 675 = 3^3 * 5^2 and 676 = 2^2 * 13^2 are the smallest products of at least 2 composite prime powers that differ by 1.
a(2) = 9800 since  (3^4 * 11^2) - (2^3 * 5^2 * 7^2) = 1.
a(3) = 235224 since (5^2 * 97^2) - (2^3 * 3^5 * 11^2) = 1.

Mathematica

nn = 2^36; s = Select[Rest@ Union@ Flatten@ Table[a^2*b^3, {b, nn^(1/3)}, {a, Sqrt[nn/b^3]}], ! PrimePowerQ[#] &]; Map[s[[#]] &, Position[Differences[s], 1][[All, 1]] ]

Crossrefs

Cf. A286708, A358173.

Sequence in context: A158393 A294949 A159208 * A173134 A258963 A309787

Adjacent sequences: A358171 A358172 A358173 * A358175 A358176 A358177

Keyword

nonn

Author

Michael De Vlieger, Nov 01 2022

Status

approved